Question 24249: Exact Finite Exponential Sums Are Not General Infinite-Value Certificates

Original question and givens

Use the whole real series E(x)=sum over n≥0 of x^n/n!, with power-series coefficients1/n!. A finite sum is a separate object; whole-series identities require the declared convergence and rearrangement obligations. Use exact x=24/25, cutoff=28, including terms0 through cutoff. Give (x, cutoff, terms, partial_sums, finite_sum, infinite_value_certificate, boundary).

• G001 — Use the whole real series E(x)=sum over n≥0 of x^n/n!, with power-series coefficients1/n!. A finite sum is a separate object; whole-series identities require the declared convergence and rearrangement obligations. Use exact x=24/25, cutoff=28, including terms0 through cutoff. Give (x, cutoff, terms, partial_sums, finite_sum, infinite_value_certificate, boundary).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-real-exponential-function

Step-by-step derivation

source roles = [exp-finite-partial-sum]

derived = [[x, cutoff, terms, partial_sums, finite_sum, infinite_value_certificate, boundary]]

source roles = [0]

derived = [1]

(24/25)^0

Exp ORIGINAL x power0 = 1

Exp term0 power over factorial := div(1, 1)

Exp term0 power over factorial = 1

Exp cumulative sum through0 := sum(0, 1)

Exp cumulative sum through0 = 1

Exp term1 factorial step1 := mul(1, 1)

Exp term1 factorial step1 = 1

(24/25)^1

Exp ORIGINAL x power1 = 24/25

Exp term1 power over factorial := div(24/25, 1)

Exp term1 power over factorial = 24/25

Exp cumulative sum through1 := sum(1, 24/25)

Exp cumulative sum through1 = 49/25

Exp term2 factorial step1 := mul(1, 1)

Exp term2 factorial step1 = 1

Exp term2 factorial step2 := mul(1, 2)

Exp term2 factorial step2 = 2

(24/25)^2

Exp ORIGINAL x power2 = 576/625

Exp term2 power over factorial := div(576/625, 2)

Exp term2 power over factorial = 288/625

Exp cumulative sum through2 := sum(49/25, 288/625)

Exp cumulative sum through2 = 1513/625

Exp term3 factorial step1 := mul(1, 1)

Exp term3 factorial step1 = 1

Exp term3 factorial step2 := mul(1, 2)

Exp term3 factorial step2 = 2

Exp term3 factorial step3 := mul(2, 3)

Exp term3 factorial step3 = 6

(24/25)^3

Exp ORIGINAL x power3 = 13824/15625

Exp term3 power over factorial := div(13824/15625, 6)

Exp term3 power over factorial = 2304/15625

Exp cumulative sum through3 := sum(1513/625, 2304/15625)

Exp cumulative sum through3 = 40129/15625

Exp term4 factorial step1 := mul(1, 1)

Exp term4 factorial step1 = 1

Exp term4 factorial step2 := mul(1, 2)

Exp term4 factorial step2 = 2

Exp term4 factorial step3 := mul(2, 3)

Exp term4 factorial step3 = 6

Exp term4 factorial step4 := mul(6, 4)

Exp term4 factorial step4 = 24

(24/25)^4

Exp ORIGINAL x power4 = 331776/390625

Exp term4 power over factorial := div(331776/390625, 24)

Exp term4 power over factorial = 13824/390625

Exp cumulative sum through4 := sum(40129/15625, 13824/390625)

Exp cumulative sum through4 = 1017049/390625

Exp term5 factorial step1 := mul(1, 1)

Exp term5 factorial step1 = 1

Exp term5 factorial step2 := mul(1, 2)

Exp term5 factorial step2 = 2

Exp term5 factorial step3 := mul(2, 3)

Exp term5 factorial step3 = 6

Exp term5 factorial step4 := mul(6, 4)

Exp term5 factorial step4 = 24

Exp term5 factorial step5 := mul(24, 5)

Exp term5 factorial step5 = 120

(24/25)^5

Exp ORIGINAL x power5 = 7962624/9765625

Exp term5 power over factorial := div(7962624/9765625, 120)

Exp term5 power over factorial = 331776/48828125

Exp cumulative sum through5 := sum(1017049/390625, 331776/48828125)

Exp cumulative sum through5 = 127462901/48828125

Exp term6 factorial step1 := mul(1, 1)

Exp term6 factorial step1 = 1

Exp term6 factorial step2 := mul(1, 2)

Exp term6 factorial step2 = 2

Exp term6 factorial step3 := mul(2, 3)

Exp term6 factorial step3 = 6

Exp term6 factorial step4 := mul(6, 4)

Exp term6 factorial step4 = 24

Exp term6 factorial step5 := mul(24, 5)

Exp term6 factorial step5 = 120

Exp term6 factorial step6 := mul(120, 6)

Exp term6 factorial step6 = 720

(24/25)^6

Exp ORIGINAL x power6 = 191102976/244140625

Exp term6 power over factorial := div(191102976/244140625, 720)

Exp term6 power over factorial = 1327104/1220703125

Exp cumulative sum through6 := sum(127462901/48828125, 1327104/1220703125)

Exp cumulative sum through6 = 3187899629/1220703125

Exp term7 factorial step1 := mul(1, 1)

Exp term7 factorial step1 = 1

Exp term7 factorial step2 := mul(1, 2)

Exp term7 factorial step2 = 2

Exp term7 factorial step3 := mul(2, 3)

Exp term7 factorial step3 = 6

Exp term7 factorial step4 := mul(6, 4)

Exp term7 factorial step4 = 24

Exp term7 factorial step5 := mul(24, 5)

Exp term7 factorial step5 = 120

Exp term7 factorial step6 := mul(120, 6)

Exp term7 factorial step6 = 720

Exp term7 factorial step7 := mul(720, 7)

Exp term7 factorial step7 = 5040

(24/25)^7

Exp ORIGINAL x power7 = 4586471424/6103515625

Exp term7 power over factorial := div(4586471424/6103515625, 5040)

Exp term7 power over factorial = 31850496/213623046875

Exp cumulative sum through7 := sum(3187899629/1220703125, 31850496/213623046875)

Exp cumulative sum through7 = 557914285571/213623046875

Exp term8 factorial step1 := mul(1, 1)

Exp term8 factorial step1 = 1

Exp term8 factorial step2 := mul(1, 2)

Exp term8 factorial step2 = 2

Exp term8 factorial step3 := mul(2, 3)

Exp term8 factorial step3 = 6

Exp term8 factorial step4 := mul(6, 4)

Exp term8 factorial step4 = 24

Exp term8 factorial step5 := mul(24, 5)

Exp term8 factorial step5 = 120

Exp term8 factorial step6 := mul(120, 6)

Exp term8 factorial step6 = 720

Exp term8 factorial step7 := mul(720, 7)

Exp term8 factorial step7 = 5040

Exp term8 factorial step8 := mul(5040, 8)

Exp term8 factorial step8 = 40320

(24/25)^8

Exp ORIGINAL x power8 = 110075314176/152587890625

Exp term8 power over factorial := div(110075314176/152587890625, 40320)

Exp term8 power over factorial = 95551488/5340576171875

Exp cumulative sum through8 := sum(557914285571/213623046875, 95551488/5340576171875)

Exp cumulative sum through8 = 1992564670109/762939453125

Exp term9 factorial step1 := mul(1, 1)

Exp term9 factorial step1 = 1

Exp term9 factorial step2 := mul(1, 2)

Exp term9 factorial step2 = 2

Exp term9 factorial step3 := mul(2, 3)

Exp term9 factorial step3 = 6

Exp term9 factorial step4 := mul(6, 4)

Exp term9 factorial step4 = 24

Exp term9 factorial step5 := mul(24, 5)

Exp term9 factorial step5 = 120

Exp term9 factorial step6 := mul(120, 6)

Exp term9 factorial step6 = 720

Exp term9 factorial step7 := mul(720, 7)

Exp term9 factorial step7 = 5040

Exp term9 factorial step8 := mul(5040, 8)

Exp term9 factorial step8 = 40320

Exp term9 factorial step9 := mul(40320, 9)

Exp term9 factorial step9 = 362880

(24/25)^9

Exp ORIGINAL x power9 = 2641807540224/3814697265625

Exp term9 power over factorial := div(2641807540224/3814697265625, 362880)

Exp term9 power over factorial = 254803968/133514404296875

Exp cumulative sum through9 := sum(1992564670109/762939453125, 254803968/133514404296875)

Exp cumulative sum through9 = 348699072073043/133514404296875

Exp term10 factorial step1 := mul(1, 1)

Exp term10 factorial step1 = 1

Exp term10 factorial step2 := mul(1, 2)

Exp term10 factorial step2 = 2

Exp term10 factorial step3 := mul(2, 3)

Exp term10 factorial step3 = 6

Exp term10 factorial step4 := mul(6, 4)

Exp term10 factorial step4 = 24

Exp term10 factorial step5 := mul(24, 5)

Exp term10 factorial step5 = 120

Exp term10 factorial step6 := mul(120, 6)

Exp term10 factorial step6 = 720

Exp term10 factorial step7 := mul(720, 7)

Exp term10 factorial step7 = 5040

Exp term10 factorial step8 := mul(5040, 8)

Exp term10 factorial step8 = 40320

Exp term10 factorial step9 := mul(40320, 9)

Exp term10 factorial step9 = 362880

Exp term10 factorial step10 := mul(362880, 10)

Exp term10 factorial step10 = 3628800

(24/25)^10

Exp ORIGINAL x power10 = 63403380965376/95367431640625

Exp term10 power over factorial := div(63403380965376/95367431640625, 3628800)

Exp term10 power over factorial = 3057647616/16689300537109375

Exp cumulative sum through10 := sum(348699072073043/133514404296875, 3057647616/16689300537109375)

Exp cumulative sum through10 = 43587387066777991/16689300537109375

Exp term11 factorial step1 := mul(1, 1)

Exp term11 factorial step1 = 1

Exp term11 factorial step2 := mul(1, 2)

Exp term11 factorial step2 = 2

Exp term11 factorial step3 := mul(2, 3)

Exp term11 factorial step3 = 6

Exp term11 factorial step4 := mul(6, 4)

Exp term11 factorial step4 = 24

Exp term11 factorial step5 := mul(24, 5)

Exp term11 factorial step5 = 120

Exp term11 factorial step6 := mul(120, 6)

Exp term11 factorial step6 = 720

Exp term11 factorial step7 := mul(720, 7)

Exp term11 factorial step7 = 5040

Exp term11 factorial step8 := mul(5040, 8)

Exp term11 factorial step8 = 40320

Exp term11 factorial step9 := mul(40320, 9)

Exp term11 factorial step9 = 362880

Exp term11 factorial step10 := mul(362880, 10)

Exp term11 factorial step10 = 3628800

Exp term11 factorial step11 := mul(3628800, 11)

Exp term11 factorial step11 = 39916800

(24/25)^11

Exp ORIGINAL x power11 = 1521681143169024/2384185791015625

Exp term11 power over factorial := div(1521681143169024/2384185791015625, 39916800)

Exp term11 power over factorial = 73383542784/4589557647705078125

Exp cumulative sum through11 := sum(43587387066777991/16689300537109375, 73383542784/4589557647705078125)

Exp cumulative sum through11 = 11986531516747490309/4589557647705078125

Exp term12 factorial step1 := mul(1, 1)

Exp term12 factorial step1 = 1

Exp term12 factorial step2 := mul(1, 2)

Exp term12 factorial step2 = 2

Exp term12 factorial step3 := mul(2, 3)

Exp term12 factorial step3 = 6

Exp term12 factorial step4 := mul(6, 4)

Exp term12 factorial step4 = 24

Exp term12 factorial step5 := mul(24, 5)

Exp term12 factorial step5 = 120

Exp term12 factorial step6 := mul(120, 6)

Exp term12 factorial step6 = 720

Exp term12 factorial step7 := mul(720, 7)

Exp term12 factorial step7 = 5040

Exp term12 factorial step8 := mul(5040, 8)

Exp term12 factorial step8 = 40320

Exp term12 factorial step9 := mul(40320, 9)

Exp term12 factorial step9 = 362880

Exp term12 factorial step10 := mul(362880, 10)

Exp term12 factorial step10 = 3628800

Exp term12 factorial step11 := mul(3628800, 11)

Exp term12 factorial step11 = 39916800

Exp term12 factorial step12 := mul(39916800, 12)

Exp term12 factorial step12 = 479001600

(24/25)^12

Exp ORIGINAL x power12 = 36520347436056576/59604644775390625

Exp term12 power over factorial := div(36520347436056576/59604644775390625, 479001600)

Exp term12 power over factorial = 146767085568/114738941192626953125

Exp cumulative sum through12 := sum(11986531516747490309/4589557647705078125, 146767085568/114738941192626953125)

Exp cumulative sum through12 = 299663288065454343293/114738941192626953125

Exp term13 factorial step1 := mul(1, 1)

Exp term13 factorial step1 = 1

Exp term13 factorial step2 := mul(1, 2)

Exp term13 factorial step2 = 2

Exp term13 factorial step3 := mul(2, 3)

Exp term13 factorial step3 = 6

Exp term13 factorial step4 := mul(6, 4)

Exp term13 factorial step4 = 24

Exp term13 factorial step5 := mul(24, 5)

Exp term13 factorial step5 = 120

Exp term13 factorial step6 := mul(120, 6)

Exp term13 factorial step6 = 720

Exp term13 factorial step7 := mul(720, 7)

Exp term13 factorial step7 = 5040

Exp term13 factorial step8 := mul(5040, 8)

Exp term13 factorial step8 = 40320

Exp term13 factorial step9 := mul(40320, 9)

Exp term13 factorial step9 = 362880

Exp term13 factorial step10 := mul(362880, 10)

Exp term13 factorial step10 = 3628800

Exp term13 factorial step11 := mul(3628800, 11)

Exp term13 factorial step11 = 39916800

Exp term13 factorial step12 := mul(39916800, 12)

Exp term13 factorial step12 = 479001600

Exp term13 factorial step13 := mul(479001600, 13)

Exp term13 factorial step13 = 6227020800

(24/25)^13

Exp ORIGINAL x power13 = 876488338465357824/1490116119384765625

Exp term13 power over factorial := div(876488338465357824/1490116119384765625, 6227020800)

Exp term13 power over factorial = 3522410053632/37290155887603759765625

Exp cumulative sum through13 := sum(299663288065454343293/114738941192626953125, 3522410053632/37290155887603759765625)

Exp cumulative sum through13 = 97390568624795071623857/37290155887603759765625

Exp term14 factorial step1 := mul(1, 1)

Exp term14 factorial step1 = 1

Exp term14 factorial step2 := mul(1, 2)

Exp term14 factorial step2 = 2

Exp term14 factorial step3 := mul(2, 3)

Exp term14 factorial step3 = 6

Exp term14 factorial step4 := mul(6, 4)

Exp term14 factorial step4 = 24

Exp term14 factorial step5 := mul(24, 5)

Exp term14 factorial step5 = 120

Exp term14 factorial step6 := mul(120, 6)

Exp term14 factorial step6 = 720

Exp term14 factorial step7 := mul(720, 7)

Exp term14 factorial step7 = 5040

Exp term14 factorial step8 := mul(5040, 8)

Exp term14 factorial step8 = 40320

Exp term14 factorial step9 := mul(40320, 9)

Exp term14 factorial step9 = 362880

Exp term14 factorial step10 := mul(362880, 10)

Exp term14 factorial step10 = 3628800

Exp term14 factorial step11 := mul(3628800, 11)

Exp term14 factorial step11 = 39916800

Exp term14 factorial step12 := mul(39916800, 12)

Exp term14 factorial step12 = 479001600

Exp term14 factorial step13 := mul(479001600, 13)

Exp term14 factorial step13 = 6227020800

Exp term14 factorial step14 := mul(6227020800, 14)

Exp term14 factorial step14 = 87178291200

(24/25)^14

Exp ORIGINAL x power14 = 21035720123168587776/37252902984619140625

Exp term14 power over factorial := div(21035720123168587776/37252902984619140625, 87178291200)

Exp term14 power over factorial = 42268920643584/6525777280330657958984375

Exp cumulative sum through14 := sum(97390568624795071623857/37290155887603759765625, 42268920643584/6525777280330657958984375)

Exp cumulative sum through14 = 17043349509381406454818559/6525777280330657958984375

Exp term15 factorial step1 := mul(1, 1)

Exp term15 factorial step1 = 1

Exp term15 factorial step2 := mul(1, 2)

Exp term15 factorial step2 = 2

Exp term15 factorial step3 := mul(2, 3)

Exp term15 factorial step3 = 6

Exp term15 factorial step4 := mul(6, 4)

Exp term15 factorial step4 = 24

Exp term15 factorial step5 := mul(24, 5)

Exp term15 factorial step5 = 120

Exp term15 factorial step6 := mul(120, 6)

Exp term15 factorial step6 = 720

Exp term15 factorial step7 := mul(720, 7)

Exp term15 factorial step7 = 5040

Exp term15 factorial step8 := mul(5040, 8)

Exp term15 factorial step8 = 40320

Exp term15 factorial step9 := mul(40320, 9)

Exp term15 factorial step9 = 362880

Exp term15 factorial step10 := mul(362880, 10)

Exp term15 factorial step10 = 3628800

Exp term15 factorial step11 := mul(3628800, 11)

Exp term15 factorial step11 = 39916800

Exp term15 factorial step12 := mul(39916800, 12)

Exp term15 factorial step12 = 479001600

Exp term15 factorial step13 := mul(479001600, 13)

Exp term15 factorial step13 = 6227020800

Exp term15 factorial step14 := mul(6227020800, 14)

Exp term15 factorial step14 = 87178291200

Exp term15 factorial step15 := mul(87178291200, 15)

Exp term15 factorial step15 = 1307674368000

(24/25)^15

Exp ORIGINAL x power15 = 504857282956046106624/931322574615478515625

Exp term15 power over factorial := div(504857282956046106624/931322574615478515625, 1307674368000)

Exp term15 power over factorial = 338151365148672/815722160041332244873046875

Exp cumulative sum through15 := sum(17043349509381406454818559/6525777280330657958984375, 338151365148672/815722160041332244873046875)

Exp cumulative sum through15 = 27667775177571609846980111/10593794286251068115234375

Exp term16 factorial step1 := mul(1, 1)

Exp term16 factorial step1 = 1

Exp term16 factorial step2 := mul(1, 2)

Exp term16 factorial step2 = 2

Exp term16 factorial step3 := mul(2, 3)

Exp term16 factorial step3 = 6

Exp term16 factorial step4 := mul(6, 4)

Exp term16 factorial step4 = 24

Exp term16 factorial step5 := mul(24, 5)

Exp term16 factorial step5 = 120

Exp term16 factorial step6 := mul(120, 6)

Exp term16 factorial step6 = 720

Exp term16 factorial step7 := mul(720, 7)

Exp term16 factorial step7 = 5040

Exp term16 factorial step8 := mul(5040, 8)

Exp term16 factorial step8 = 40320

Exp term16 factorial step9 := mul(40320, 9)

Exp term16 factorial step9 = 362880

Exp term16 factorial step10 := mul(362880, 10)

Exp term16 factorial step10 = 3628800

Exp term16 factorial step11 := mul(3628800, 11)

Exp term16 factorial step11 = 39916800

Exp term16 factorial step12 := mul(39916800, 12)

Exp term16 factorial step12 = 479001600

Exp term16 factorial step13 := mul(479001600, 13)

Exp term16 factorial step13 = 6227020800

Exp term16 factorial step14 := mul(6227020800, 14)

Exp term16 factorial step14 = 87178291200

Exp term16 factorial step15 := mul(87178291200, 15)

Exp term16 factorial step15 = 1307674368000

Exp term16 factorial step16 := mul(1307674368000, 16)

Exp term16 factorial step16 = 20922789888000

(24/25)^16

Exp ORIGINAL x power16 = 12116574790945106558976/23283064365386962890625

Exp term16 power over factorial := div(12116574790945106558976/23283064365386962890625, 20922789888000)

Exp term16 power over factorial = 507227047723008/20393054001033306121826171875

Exp cumulative sum through16 := sum(27667775177571609846980111/10593794286251068115234375, 507227047723008/20393054001033306121826171875)

Exp cumulative sum through16 = 53260467216825856182484436683/20393054001033306121826171875

Exp term17 factorial step1 := mul(1, 1)

Exp term17 factorial step1 = 1

Exp term17 factorial step2 := mul(1, 2)

Exp term17 factorial step2 = 2

Exp term17 factorial step3 := mul(2, 3)

Exp term17 factorial step3 = 6

Exp term17 factorial step4 := mul(6, 4)

Exp term17 factorial step4 = 24

Exp term17 factorial step5 := mul(24, 5)

Exp term17 factorial step5 = 120

Exp term17 factorial step6 := mul(120, 6)

Exp term17 factorial step6 = 720

Exp term17 factorial step7 := mul(720, 7)

Exp term17 factorial step7 = 5040

Exp term17 factorial step8 := mul(5040, 8)

Exp term17 factorial step8 = 40320

Exp term17 factorial step9 := mul(40320, 9)

Exp term17 factorial step9 = 362880

Exp term17 factorial step10 := mul(362880, 10)

Exp term17 factorial step10 = 3628800

Exp term17 factorial step11 := mul(3628800, 11)

Exp term17 factorial step11 = 39916800

Exp term17 factorial step12 := mul(39916800, 12)

Exp term17 factorial step12 = 479001600

Exp term17 factorial step13 := mul(479001600, 13)

Exp term17 factorial step13 = 6227020800

Exp term17 factorial step14 := mul(6227020800, 14)

Exp term17 factorial step14 = 87178291200

Exp term17 factorial step15 := mul(87178291200, 15)

Exp term17 factorial step15 = 1307674368000

Exp term17 factorial step16 := mul(1307674368000, 16)

Exp term17 factorial step16 = 20922789888000

Exp term17 factorial step17 := mul(20922789888000, 17)

Exp term17 factorial step17 = 355687428096000

(24/25)^17

Exp ORIGINAL x power17 = 290797794982682557415424/582076609134674072265625

Exp term17 power over factorial := div(290797794982682557415424/582076609134674072265625, 355687428096000)

Exp term17 power over factorial = 12173449145352192/8667047950439155101776123046875

Exp cumulative sum through17 := sum(53260467216825856182484436683/20393054001033306121826171875, 12173449145352192/8667047950439155101776123046875)

Exp cumulative sum through17 = 22635698567151001051005030942467/8667047950439155101776123046875

Exp term18 factorial step1 := mul(1, 1)

Exp term18 factorial step1 = 1

Exp term18 factorial step2 := mul(1, 2)

Exp term18 factorial step2 = 2

Exp term18 factorial step3 := mul(2, 3)

Exp term18 factorial step3 = 6

Exp term18 factorial step4 := mul(6, 4)

Exp term18 factorial step4 = 24

Exp term18 factorial step5 := mul(24, 5)

Exp term18 factorial step5 = 120

Exp term18 factorial step6 := mul(120, 6)

Exp term18 factorial step6 = 720

Exp term18 factorial step7 := mul(720, 7)

Exp term18 factorial step7 = 5040

Exp term18 factorial step8 := mul(5040, 8)

Exp term18 factorial step8 = 40320

Exp term18 factorial step9 := mul(40320, 9)

Exp term18 factorial step9 = 362880

Exp term18 factorial step10 := mul(362880, 10)

Exp term18 factorial step10 = 3628800

Exp term18 factorial step11 := mul(3628800, 11)

Exp term18 factorial step11 = 39916800

Exp term18 factorial step12 := mul(39916800, 12)

Exp term18 factorial step12 = 479001600

Exp term18 factorial step13 := mul(479001600, 13)

Exp term18 factorial step13 = 6227020800

Exp term18 factorial step14 := mul(6227020800, 14)

Exp term18 factorial step14 = 87178291200

Exp term18 factorial step15 := mul(87178291200, 15)

Exp term18 factorial step15 = 1307674368000

Exp term18 factorial step16 := mul(1307674368000, 16)

Exp term18 factorial step16 = 20922789888000

Exp term18 factorial step17 := mul(20922789888000, 17)

Exp term18 factorial step17 = 355687428096000

Exp term18 factorial step18 := mul(355687428096000, 18)

Exp term18 factorial step18 = 6402373705728000

(24/25)^18

Exp ORIGINAL x power18 = 6979147079584381377970176/14551915228366851806640625

Exp term18 power over factorial := div(6979147079584381377970176/14551915228366851806640625, 6402373705728000)

Exp term18 power over factorial = 16231265527136256/216676198760978877544403076171875

Exp cumulative sum through18 := sum(22635698567151001051005030942467/8667047950439155101776123046875, 16231265527136256/216676198760978877544403076171875)

Exp cumulative sum through18 = 565892464178775042506391300697931/216676198760978877544403076171875

Exp term19 factorial step1 := mul(1, 1)

Exp term19 factorial step1 = 1

Exp term19 factorial step2 := mul(1, 2)

Exp term19 factorial step2 = 2

Exp term19 factorial step3 := mul(2, 3)

Exp term19 factorial step3 = 6

Exp term19 factorial step4 := mul(6, 4)

Exp term19 factorial step4 = 24

Exp term19 factorial step5 := mul(24, 5)

Exp term19 factorial step5 = 120

Exp term19 factorial step6 := mul(120, 6)

Exp term19 factorial step6 = 720

Exp term19 factorial step7 := mul(720, 7)

Exp term19 factorial step7 = 5040

Exp term19 factorial step8 := mul(5040, 8)

Exp term19 factorial step8 = 40320

Exp term19 factorial step9 := mul(40320, 9)

Exp term19 factorial step9 = 362880

Exp term19 factorial step10 := mul(362880, 10)

Exp term19 factorial step10 = 3628800

Exp term19 factorial step11 := mul(3628800, 11)

Exp term19 factorial step11 = 39916800

Exp term19 factorial step12 := mul(39916800, 12)

Exp term19 factorial step12 = 479001600

Exp term19 factorial step13 := mul(479001600, 13)

Exp term19 factorial step13 = 6227020800

Exp term19 factorial step14 := mul(6227020800, 14)

Exp term19 factorial step14 = 87178291200

Exp term19 factorial step15 := mul(87178291200, 15)

Exp term19 factorial step15 = 1307674368000

Exp term19 factorial step16 := mul(1307674368000, 16)

Exp term19 factorial step16 = 20922789888000

Exp term19 factorial step17 := mul(20922789888000, 17)

Exp term19 factorial step17 = 355687428096000

Exp term19 factorial step18 := mul(355687428096000, 18)

Exp term19 factorial step18 = 6402373705728000

Exp term19 factorial step19 := mul(6402373705728000, 19)

Exp term19 factorial step19 = 121645100408832000

(24/25)^19

Exp ORIGINAL x power19 = 167499529910025153071284224/363797880709171295166015625

Exp term19 power over factorial := div(167499529910025153071284224/363797880709171295166015625, 121645100408832000)

Exp term19 power over factorial = 389550372651270144/102921194411464966833591461181640625

Exp cumulative sum through19 := sum(565892464178775042506391300697931/216676198760978877544403076171875, 389550372651270144/102921194411464966833591461181640625)

Exp cumulative sum through19 = 15811701204995185034122720028399257/6054187906556762754917144775390625

Exp term20 factorial step1 := mul(1, 1)

Exp term20 factorial step1 = 1

Exp term20 factorial step2 := mul(1, 2)

Exp term20 factorial step2 = 2

Exp term20 factorial step3 := mul(2, 3)

Exp term20 factorial step3 = 6

Exp term20 factorial step4 := mul(6, 4)

Exp term20 factorial step4 = 24

Exp term20 factorial step5 := mul(24, 5)

Exp term20 factorial step5 = 120

Exp term20 factorial step6 := mul(120, 6)

Exp term20 factorial step6 = 720

Exp term20 factorial step7 := mul(720, 7)

Exp term20 factorial step7 = 5040

Exp term20 factorial step8 := mul(5040, 8)

Exp term20 factorial step8 = 40320

Exp term20 factorial step9 := mul(40320, 9)

Exp term20 factorial step9 = 362880

Exp term20 factorial step10 := mul(362880, 10)

Exp term20 factorial step10 = 3628800

Exp term20 factorial step11 := mul(3628800, 11)

Exp term20 factorial step11 = 39916800

Exp term20 factorial step12 := mul(39916800, 12)

Exp term20 factorial step12 = 479001600

Exp term20 factorial step13 := mul(479001600, 13)

Exp term20 factorial step13 = 6227020800

Exp term20 factorial step14 := mul(6227020800, 14)

Exp term20 factorial step14 = 87178291200

Exp term20 factorial step15 := mul(87178291200, 15)

Exp term20 factorial step15 = 1307674368000

Exp term20 factorial step16 := mul(1307674368000, 16)

Exp term20 factorial step16 = 20922789888000

Exp term20 factorial step17 := mul(20922789888000, 17)

Exp term20 factorial step17 = 355687428096000

Exp term20 factorial step18 := mul(355687428096000, 18)

Exp term20 factorial step18 = 6402373705728000

Exp term20 factorial step19 := mul(6402373705728000, 19)

Exp term20 factorial step19 = 121645100408832000

Exp term20 factorial step20 := mul(121645100408832000, 20)

Exp term20 factorial step20 = 2432902008176640000

(24/25)^20

Exp ORIGINAL x power20 = 4019988717840603673710821376/9094947017729282379150390625

Exp term20 power over factorial := div(4019988717840603673710821376/9094947017729282379150390625, 2432902008176640000)

Exp term20 power over factorial = 2337302235907620864/12865149301433120854198932647705078125

Exp cumulative sum through20 := sum(15811701204995185034122720028399257/6054187906556762754917144775390625, 2337302235907620864/12865149301433120854198932647705078125)

Exp cumulative sum through20 = 33599865060614768199848082296256041989/12865149301433120854198932647705078125

Exp term21 factorial step1 := mul(1, 1)

Exp term21 factorial step1 = 1

Exp term21 factorial step2 := mul(1, 2)

Exp term21 factorial step2 = 2

Exp term21 factorial step3 := mul(2, 3)

Exp term21 factorial step3 = 6

Exp term21 factorial step4 := mul(6, 4)

Exp term21 factorial step4 = 24

Exp term21 factorial step5 := mul(24, 5)

Exp term21 factorial step5 = 120

Exp term21 factorial step6 := mul(120, 6)

Exp term21 factorial step6 = 720

Exp term21 factorial step7 := mul(720, 7)

Exp term21 factorial step7 = 5040

Exp term21 factorial step8 := mul(5040, 8)

Exp term21 factorial step8 = 40320

Exp term21 factorial step9 := mul(40320, 9)

Exp term21 factorial step9 = 362880

Exp term21 factorial step10 := mul(362880, 10)

Exp term21 factorial step10 = 3628800

Exp term21 factorial step11 := mul(3628800, 11)

Exp term21 factorial step11 = 39916800

Exp term21 factorial step12 := mul(39916800, 12)

Exp term21 factorial step12 = 479001600

Exp term21 factorial step13 := mul(479001600, 13)

Exp term21 factorial step13 = 6227020800

Exp term21 factorial step14 := mul(6227020800, 14)

Exp term21 factorial step14 = 87178291200

Exp term21 factorial step15 := mul(87178291200, 15)

Exp term21 factorial step15 = 1307674368000

Exp term21 factorial step16 := mul(1307674368000, 16)

Exp term21 factorial step16 = 20922789888000

Exp term21 factorial step17 := mul(20922789888000, 17)

Exp term21 factorial step17 = 355687428096000

Exp term21 factorial step18 := mul(355687428096000, 18)

Exp term21 factorial step18 = 6402373705728000

Exp term21 factorial step19 := mul(6402373705728000, 19)

Exp term21 factorial step19 = 121645100408832000

Exp term21 factorial step20 := mul(121645100408832000, 20)

Exp term21 factorial step20 = 2432902008176640000

Exp term21 factorial step21 := mul(2432902008176640000, 21)

Exp term21 factorial step21 = 51090942171709440000

(24/25)^21

Exp ORIGINAL x power21 = 96479729228174488169059713024/227373675443232059478759765625

Exp term21 power over factorial := div(96479729228174488169059713024/227373675443232059478759765625, 51090942171709440000)

Exp term21 power over factorial = 18698417887260966912/2251401127750796149484813213348388671875

Exp cumulative sum through21 := sum(33599865060614768199848082296256041989/12865149301433120854198932647705078125, 18698417887260966912/2251401127750796149484813213348388671875)

Exp cumulative sum through21 = 452305875815968033460931755364005254999/173184702134676626883447170257568359375

Exp term22 factorial step1 := mul(1, 1)

Exp term22 factorial step1 = 1

Exp term22 factorial step2 := mul(1, 2)

Exp term22 factorial step2 = 2

Exp term22 factorial step3 := mul(2, 3)

Exp term22 factorial step3 = 6

Exp term22 factorial step4 := mul(6, 4)

Exp term22 factorial step4 = 24

Exp term22 factorial step5 := mul(24, 5)

Exp term22 factorial step5 = 120

Exp term22 factorial step6 := mul(120, 6)

Exp term22 factorial step6 = 720

Exp term22 factorial step7 := mul(720, 7)

Exp term22 factorial step7 = 5040

Exp term22 factorial step8 := mul(5040, 8)

Exp term22 factorial step8 = 40320

Exp term22 factorial step9 := mul(40320, 9)

Exp term22 factorial step9 = 362880

Exp term22 factorial step10 := mul(362880, 10)

Exp term22 factorial step10 = 3628800

Exp term22 factorial step11 := mul(3628800, 11)

Exp term22 factorial step11 = 39916800

Exp term22 factorial step12 := mul(39916800, 12)

Exp term22 factorial step12 = 479001600

Exp term22 factorial step13 := mul(479001600, 13)

Exp term22 factorial step13 = 6227020800

Exp term22 factorial step14 := mul(6227020800, 14)

Exp term22 factorial step14 = 87178291200

Exp term22 factorial step15 := mul(87178291200, 15)

Exp term22 factorial step15 = 1307674368000

Exp term22 factorial step16 := mul(1307674368000, 16)

Exp term22 factorial step16 = 20922789888000

Exp term22 factorial step17 := mul(20922789888000, 17)

Exp term22 factorial step17 = 355687428096000

Exp term22 factorial step18 := mul(355687428096000, 18)

Exp term22 factorial step18 = 6402373705728000

Exp term22 factorial step19 := mul(6402373705728000, 19)

Exp term22 factorial step19 = 121645100408832000

Exp term22 factorial step20 := mul(121645100408832000, 20)

Exp term22 factorial step20 = 2432902008176640000

Exp term22 factorial step21 := mul(2432902008176640000, 21)

Exp term22 factorial step21 = 51090942171709440000

Exp term22 factorial step22 := mul(51090942171709440000, 22)

Exp term22 factorial step22 = 1124000727777607680000

(24/25)^22

Exp ORIGINAL x power22 = 2315513501476187716057433112576/5684341886080801486968994140625

Exp term22 power over factorial := div(2315513501476187716057433112576/5684341886080801486968994140625, 1124000727777607680000)

Exp term22 power over factorial = 224381014647131602944/619135310131468941108323633670806884765625

Exp cumulative sum through22 := sum(452305875815968033460931755364005254999/173184702134676626883447170257568359375, 224381014647131602944/619135310131468941108323633670806884765625)

Exp cumulative sum through22 = 230999072291726531374722200920137988317767/88447901447352705872617661952972412109375

Exp term23 factorial step1 := mul(1, 1)

Exp term23 factorial step1 = 1

Exp term23 factorial step2 := mul(1, 2)

Exp term23 factorial step2 = 2

Exp term23 factorial step3 := mul(2, 3)

Exp term23 factorial step3 = 6

Exp term23 factorial step4 := mul(6, 4)

Exp term23 factorial step4 = 24

Exp term23 factorial step5 := mul(24, 5)

Exp term23 factorial step5 = 120

Exp term23 factorial step6 := mul(120, 6)

Exp term23 factorial step6 = 720

Exp term23 factorial step7 := mul(720, 7)

Exp term23 factorial step7 = 5040

Exp term23 factorial step8 := mul(5040, 8)

Exp term23 factorial step8 = 40320

Exp term23 factorial step9 := mul(40320, 9)

Exp term23 factorial step9 = 362880

Exp term23 factorial step10 := mul(362880, 10)

Exp term23 factorial step10 = 3628800

Exp term23 factorial step11 := mul(3628800, 11)

Exp term23 factorial step11 = 39916800

Exp term23 factorial step12 := mul(39916800, 12)

Exp term23 factorial step12 = 479001600

Exp term23 factorial step13 := mul(479001600, 13)

Exp term23 factorial step13 = 6227020800

Exp term23 factorial step14 := mul(6227020800, 14)

Exp term23 factorial step14 = 87178291200

Exp term23 factorial step15 := mul(87178291200, 15)

Exp term23 factorial step15 = 1307674368000

Exp term23 factorial step16 := mul(1307674368000, 16)

Exp term23 factorial step16 = 20922789888000

Exp term23 factorial step17 := mul(20922789888000, 17)

Exp term23 factorial step17 = 355687428096000

Exp term23 factorial step18 := mul(355687428096000, 18)

Exp term23 factorial step18 = 6402373705728000

Exp term23 factorial step19 := mul(6402373705728000, 19)

Exp term23 factorial step19 = 121645100408832000

Exp term23 factorial step20 := mul(121645100408832000, 20)

Exp term23 factorial step20 = 2432902008176640000

Exp term23 factorial step21 := mul(2432902008176640000, 21)

Exp term23 factorial step21 = 51090942171709440000

Exp term23 factorial step22 := mul(51090942171709440000, 22)

Exp term23 factorial step22 = 1124000727777607680000

Exp term23 factorial step23 := mul(1124000727777607680000, 23)

Exp term23 factorial step23 = 25852016738884976640000

(24/25)^23

Exp ORIGINAL x power23 = 55572324035428505185378394701824/142108547152020037174224853515625

Exp term23 power over factorial := div(55572324035428505185378394701824/142108547152020037174224853515625, 25852016738884976640000)

Exp term23 power over factorial = 5385144351531158470656/356002803325594641137286089360713958740234375

Exp cumulative sum through23 := sum(230999072291726531374722200920137988317767/88447901447352705872617661952972412109375, 5385144351531158470656/356002803325594641137286089360713958740234375)

Exp cumulative sum through23 = 929771265974199288783262243847906934137482831/356002803325594641137286089360713958740234375

Exp term24 factorial step1 := mul(1, 1)

Exp term24 factorial step1 = 1

Exp term24 factorial step2 := mul(1, 2)

Exp term24 factorial step2 = 2

Exp term24 factorial step3 := mul(2, 3)

Exp term24 factorial step3 = 6

Exp term24 factorial step4 := mul(6, 4)

Exp term24 factorial step4 = 24

Exp term24 factorial step5 := mul(24, 5)

Exp term24 factorial step5 = 120

Exp term24 factorial step6 := mul(120, 6)

Exp term24 factorial step6 = 720

Exp term24 factorial step7 := mul(720, 7)

Exp term24 factorial step7 = 5040

Exp term24 factorial step8 := mul(5040, 8)

Exp term24 factorial step8 = 40320

Exp term24 factorial step9 := mul(40320, 9)

Exp term24 factorial step9 = 362880

Exp term24 factorial step10 := mul(362880, 10)

Exp term24 factorial step10 = 3628800

Exp term24 factorial step11 := mul(3628800, 11)

Exp term24 factorial step11 = 39916800

Exp term24 factorial step12 := mul(39916800, 12)

Exp term24 factorial step12 = 479001600

Exp term24 factorial step13 := mul(479001600, 13)

Exp term24 factorial step13 = 6227020800

Exp term24 factorial step14 := mul(6227020800, 14)

Exp term24 factorial step14 = 87178291200

Exp term24 factorial step15 := mul(87178291200, 15)

Exp term24 factorial step15 = 1307674368000

Exp term24 factorial step16 := mul(1307674368000, 16)

Exp term24 factorial step16 = 20922789888000

Exp term24 factorial step17 := mul(20922789888000, 17)

Exp term24 factorial step17 = 355687428096000

Exp term24 factorial step18 := mul(355687428096000, 18)

Exp term24 factorial step18 = 6402373705728000

Exp term24 factorial step19 := mul(6402373705728000, 19)

Exp term24 factorial step19 = 121645100408832000

Exp term24 factorial step20 := mul(121645100408832000, 20)

Exp term24 factorial step20 = 2432902008176640000

Exp term24 factorial step21 := mul(2432902008176640000, 21)

Exp term24 factorial step21 = 51090942171709440000

Exp term24 factorial step22 := mul(51090942171709440000, 22)

Exp term24 factorial step22 = 1124000727777607680000

Exp term24 factorial step23 := mul(1124000727777607680000, 23)

Exp term24 factorial step23 = 25852016738884976640000

Exp term24 factorial step24 := mul(25852016738884976640000, 24)

Exp term24 factorial step24 = 620448401733239439360000

(24/25)^24

Exp ORIGINAL x power24 = 1333735776850284124449081472843776/3552713678800500929355621337890625

Exp term24 power over factorial := div(1333735776850284124449081472843776/3552713678800500929355621337890625, 620448401733239439360000)

Exp term24 power over factorial = 5385144351531158470656/8900070083139866028432152234017848968505859375

Exp cumulative sum through24 := sum(929771265974199288783262243847906934137482831/356002803325594641137286089360713958740234375, 5385144351531158470656/8900070083139866028432152234017848968505859375)

Exp cumulative sum through24 = 23244281649354982219581561481342024884595541431/8900070083139866028432152234017848968505859375

Exp term25 factorial step1 := mul(1, 1)

Exp term25 factorial step1 = 1

Exp term25 factorial step2 := mul(1, 2)

Exp term25 factorial step2 = 2

Exp term25 factorial step3 := mul(2, 3)

Exp term25 factorial step3 = 6

Exp term25 factorial step4 := mul(6, 4)

Exp term25 factorial step4 = 24

Exp term25 factorial step5 := mul(24, 5)

Exp term25 factorial step5 = 120

Exp term25 factorial step6 := mul(120, 6)

Exp term25 factorial step6 = 720

Exp term25 factorial step7 := mul(720, 7)

Exp term25 factorial step7 = 5040

Exp term25 factorial step8 := mul(5040, 8)

Exp term25 factorial step8 = 40320

Exp term25 factorial step9 := mul(40320, 9)

Exp term25 factorial step9 = 362880

Exp term25 factorial step10 := mul(362880, 10)

Exp term25 factorial step10 = 3628800

Exp term25 factorial step11 := mul(3628800, 11)

Exp term25 factorial step11 = 39916800

Exp term25 factorial step12 := mul(39916800, 12)

Exp term25 factorial step12 = 479001600

Exp term25 factorial step13 := mul(479001600, 13)

Exp term25 factorial step13 = 6227020800

Exp term25 factorial step14 := mul(6227020800, 14)

Exp term25 factorial step14 = 87178291200

Exp term25 factorial step15 := mul(87178291200, 15)

Exp term25 factorial step15 = 1307674368000

Exp term25 factorial step16 := mul(1307674368000, 16)

Exp term25 factorial step16 = 20922789888000

Exp term25 factorial step17 := mul(20922789888000, 17)

Exp term25 factorial step17 = 355687428096000

Exp term25 factorial step18 := mul(355687428096000, 18)

Exp term25 factorial step18 = 6402373705728000

Exp term25 factorial step19 := mul(6402373705728000, 19)

Exp term25 factorial step19 = 121645100408832000

Exp term25 factorial step20 := mul(121645100408832000, 20)

Exp term25 factorial step20 = 2432902008176640000

Exp term25 factorial step21 := mul(2432902008176640000, 21)

Exp term25 factorial step21 = 51090942171709440000

Exp term25 factorial step22 := mul(51090942171709440000, 22)

Exp term25 factorial step22 = 1124000727777607680000

Exp term25 factorial step23 := mul(1124000727777607680000, 23)

Exp term25 factorial step23 = 25852016738884976640000

Exp term25 factorial step24 := mul(25852016738884976640000, 24)

Exp term25 factorial step24 = 620448401733239439360000

Exp term25 factorial step25 := mul(620448401733239439360000, 25)

Exp term25 factorial step25 = 15511210043330985984000000

(24/25)^25

Exp ORIGINAL x power25 = 32009658644406818986777955348250624/88817841970012523233890533447265625

Exp term25 power over factorial := div(32009658644406818986777955348250624/88817841970012523233890533447265625, 15511210043330985984000000)

Exp term25 power over factorial = 129243464436747803295744/5562543801962416267770095146261155605316162109375

Exp cumulative sum through25 := sum(23244281649354982219581561481342024884595541431/8900070083139866028432152234017848968505859375, 129243464436747803295744/5562543801962416267770095146261155605316162109375)

Exp cumulative sum through25 = 44977325172900507390831195216972848265077451053/17221497838892929621579241938889026641845703125

Exp term26 factorial step1 := mul(1, 1)

Exp term26 factorial step1 = 1

Exp term26 factorial step2 := mul(1, 2)

Exp term26 factorial step2 = 2

Exp term26 factorial step3 := mul(2, 3)

Exp term26 factorial step3 = 6

Exp term26 factorial step4 := mul(6, 4)

Exp term26 factorial step4 = 24

Exp term26 factorial step5 := mul(24, 5)

Exp term26 factorial step5 = 120

Exp term26 factorial step6 := mul(120, 6)

Exp term26 factorial step6 = 720

Exp term26 factorial step7 := mul(720, 7)

Exp term26 factorial step7 = 5040

Exp term26 factorial step8 := mul(5040, 8)

Exp term26 factorial step8 = 40320

Exp term26 factorial step9 := mul(40320, 9)

Exp term26 factorial step9 = 362880

Exp term26 factorial step10 := mul(362880, 10)

Exp term26 factorial step10 = 3628800

Exp term26 factorial step11 := mul(3628800, 11)

Exp term26 factorial step11 = 39916800

Exp term26 factorial step12 := mul(39916800, 12)

Exp term26 factorial step12 = 479001600

Exp term26 factorial step13 := mul(479001600, 13)

Exp term26 factorial step13 = 6227020800

Exp term26 factorial step14 := mul(6227020800, 14)

Exp term26 factorial step14 = 87178291200

Exp term26 factorial step15 := mul(87178291200, 15)

Exp term26 factorial step15 = 1307674368000

Exp term26 factorial step16 := mul(1307674368000, 16)

Exp term26 factorial step16 = 20922789888000

Exp term26 factorial step17 := mul(20922789888000, 17)

Exp term26 factorial step17 = 355687428096000

Exp term26 factorial step18 := mul(355687428096000, 18)

Exp term26 factorial step18 = 6402373705728000

Exp term26 factorial step19 := mul(6402373705728000, 19)

Exp term26 factorial step19 = 121645100408832000

Exp term26 factorial step20 := mul(121645100408832000, 20)

Exp term26 factorial step20 = 2432902008176640000

Exp term26 factorial step21 := mul(2432902008176640000, 21)

Exp term26 factorial step21 = 51090942171709440000

Exp term26 factorial step22 := mul(51090942171709440000, 22)

Exp term26 factorial step22 = 1124000727777607680000

Exp term26 factorial step23 := mul(1124000727777607680000, 23)

Exp term26 factorial step23 = 25852016738884976640000

Exp term26 factorial step24 := mul(25852016738884976640000, 24)

Exp term26 factorial step24 = 620448401733239439360000

Exp term26 factorial step25 := mul(620448401733239439360000, 25)

Exp term26 factorial step25 = 15511210043330985984000000

Exp term26 factorial step26 := mul(15511210043330985984000000, 26)

Exp term26 factorial step26 = 403291461126605635584000000

(24/25)^26

Exp ORIGINAL x power26 = 768231807465763655682670928358014976/2220446049250313080847263336181640625

Exp term26 power over factorial := div(768231807465763655682670928358014976/2220446049250313080847263336181640625, 403291461126605635584000000)

Exp term26 power over factorial = 1550921573240973639548928/1807826735637785287025280922534875571727752685546875

Exp cumulative sum through26 := sum(44977325172900507390831195216972848265077451053/17221497838892929621579241938889026641845703125, 1550921573240973639548928/1807826735637785287025280922534875571727752685546875)

Exp cumulative sum through26 = 39020617438225047631012435697955754709648587304443/14940716823452770967151082004420459270477294921875

Exp term27 factorial step1 := mul(1, 1)

Exp term27 factorial step1 = 1

Exp term27 factorial step2 := mul(1, 2)

Exp term27 factorial step2 = 2

Exp term27 factorial step3 := mul(2, 3)

Exp term27 factorial step3 = 6

Exp term27 factorial step4 := mul(6, 4)

Exp term27 factorial step4 = 24

Exp term27 factorial step5 := mul(24, 5)

Exp term27 factorial step5 = 120

Exp term27 factorial step6 := mul(120, 6)

Exp term27 factorial step6 = 720

Exp term27 factorial step7 := mul(720, 7)

Exp term27 factorial step7 = 5040

Exp term27 factorial step8 := mul(5040, 8)

Exp term27 factorial step8 = 40320

Exp term27 factorial step9 := mul(40320, 9)

Exp term27 factorial step9 = 362880

Exp term27 factorial step10 := mul(362880, 10)

Exp term27 factorial step10 = 3628800

Exp term27 factorial step11 := mul(3628800, 11)

Exp term27 factorial step11 = 39916800

Exp term27 factorial step12 := mul(39916800, 12)

Exp term27 factorial step12 = 479001600

Exp term27 factorial step13 := mul(479001600, 13)

Exp term27 factorial step13 = 6227020800

Exp term27 factorial step14 := mul(6227020800, 14)

Exp term27 factorial step14 = 87178291200

Exp term27 factorial step15 := mul(87178291200, 15)

Exp term27 factorial step15 = 1307674368000

Exp term27 factorial step16 := mul(1307674368000, 16)

Exp term27 factorial step16 = 20922789888000

Exp term27 factorial step17 := mul(20922789888000, 17)

Exp term27 factorial step17 = 355687428096000

Exp term27 factorial step18 := mul(355687428096000, 18)

Exp term27 factorial step18 = 6402373705728000

Exp term27 factorial step19 := mul(6402373705728000, 19)

Exp term27 factorial step19 = 121645100408832000

Exp term27 factorial step20 := mul(121645100408832000, 20)

Exp term27 factorial step20 = 2432902008176640000

Exp term27 factorial step21 := mul(2432902008176640000, 21)

Exp term27 factorial step21 = 51090942171709440000

Exp term27 factorial step22 := mul(51090942171709440000, 22)

Exp term27 factorial step22 = 1124000727777607680000

Exp term27 factorial step23 := mul(1124000727777607680000, 23)

Exp term27 factorial step23 = 25852016738884976640000

Exp term27 factorial step24 := mul(25852016738884976640000, 24)

Exp term27 factorial step24 = 620448401733239439360000

Exp term27 factorial step25 := mul(620448401733239439360000, 25)

Exp term27 factorial step25 = 15511210043330985984000000

Exp term27 factorial step26 := mul(15511210043330985984000000, 26)

Exp term27 factorial step26 = 403291461126605635584000000

Exp term27 factorial step27 := mul(403291461126605635584000000, 27)

Exp term27 factorial step27 = 10888869450418352160768000000

(24/25)^27

Exp ORIGINAL x power27 = 18437563379178327736384102280592359424/55511151231257827021181583404541015625

Exp term27 power over factorial := div(18437563379178327736384102280592359424/55511151231257827021181583404541015625, 10888869450418352160768000000)

Exp term27 power over factorial = 1378596953991976568487936/45195668390944632175632023063371889293193817138671875

Exp cumulative sum through27 := sum(39020617438225047631012435697955754709648587304443/14940716823452770967151082004420459270477294921875, 1378596953991976568487936/45195668390944632175632023063371889293193817138671875)

Exp cumulative sum through27 = 118037367750630769083812617987694754950678953164428011/45195668390944632175632023063371889293193817138671875

Exp term28 factorial step1 := mul(1, 1)

Exp term28 factorial step1 = 1

Exp term28 factorial step2 := mul(1, 2)

Exp term28 factorial step2 = 2

Exp term28 factorial step3 := mul(2, 3)

Exp term28 factorial step3 = 6

Exp term28 factorial step4 := mul(6, 4)

Exp term28 factorial step4 = 24

Exp term28 factorial step5 := mul(24, 5)

Exp term28 factorial step5 = 120

Exp term28 factorial step6 := mul(120, 6)

Exp term28 factorial step6 = 720

Exp term28 factorial step7 := mul(720, 7)

Exp term28 factorial step7 = 5040

Exp term28 factorial step8 := mul(5040, 8)

Exp term28 factorial step8 = 40320

Exp term28 factorial step9 := mul(40320, 9)

Exp term28 factorial step9 = 362880

Exp term28 factorial step10 := mul(362880, 10)

Exp term28 factorial step10 = 3628800

Exp term28 factorial step11 := mul(3628800, 11)

Exp term28 factorial step11 = 39916800

Exp term28 factorial step12 := mul(39916800, 12)

Exp term28 factorial step12 = 479001600

Exp term28 factorial step13 := mul(479001600, 13)

Exp term28 factorial step13 = 6227020800

Exp term28 factorial step14 := mul(6227020800, 14)

Exp term28 factorial step14 = 87178291200

Exp term28 factorial step15 := mul(87178291200, 15)

Exp term28 factorial step15 = 1307674368000

Exp term28 factorial step16 := mul(1307674368000, 16)

Exp term28 factorial step16 = 20922789888000

Exp term28 factorial step17 := mul(20922789888000, 17)

Exp term28 factorial step17 = 355687428096000

Exp term28 factorial step18 := mul(355687428096000, 18)

Exp term28 factorial step18 = 6402373705728000

Exp term28 factorial step19 := mul(6402373705728000, 19)

Exp term28 factorial step19 = 121645100408832000

Exp term28 factorial step20 := mul(121645100408832000, 20)

Exp term28 factorial step20 = 2432902008176640000

Exp term28 factorial step21 := mul(2432902008176640000, 21)

Exp term28 factorial step21 = 51090942171709440000

Exp term28 factorial step22 := mul(51090942171709440000, 22)

Exp term28 factorial step22 = 1124000727777607680000

Exp term28 factorial step23 := mul(1124000727777607680000, 23)

Exp term28 factorial step23 = 25852016738884976640000

Exp term28 factorial step24 := mul(25852016738884976640000, 24)

Exp term28 factorial step24 = 620448401733239439360000

Exp term28 factorial step25 := mul(620448401733239439360000, 25)

Exp term28 factorial step25 = 15511210043330985984000000

Exp term28 factorial step26 := mul(15511210043330985984000000, 26)

Exp term28 factorial step26 = 403291461126605635584000000

Exp term28 factorial step27 := mul(403291461126605635584000000, 27)

Exp term28 factorial step27 = 10888869450418352160768000000

Exp term28 factorial step28 := mul(10888869450418352160768000000, 28)

Exp term28 factorial step28 = 304888344611713860501504000000

(24/25)^28

Exp ORIGINAL x power28 = 442501521100279865673218454734216626176/1387778780781445675529539585113525390625

Exp term28 power over factorial := div(442501521100279865673218454734216626176/1387778780781445675529539585113525390625, 304888344611713860501504000000)

Exp term28 power over factorial = 8271581723951859410927616/7909241968415310630735604036090080626308917999267578125

Exp cumulative sum through28 := sum(118037367750630769083812617987694754950678953164428011/45195668390944632175632023063371889293193817138671875, 8271581723951859410927616/7909241968415310630735604036090080626308917999267578125)

Exp cumulative sum through28 = 20656539356360384589667208147854853698092768663185829541/7909241968415310630735604036090080626308917999267578125

source roles = [24/25, 28, [1, 24/25, 288/625, 2304/15625, 13824/390625, 331776/48828125, 1327104/1220703125, 31850496/213623046875, 95551488/5340576171875, 254803968/133514404296875, 3057647616/16689300537109375, 73383542784/4589557647705078125, 146767085568/114738941192626953125, 3522410053632/37290155887603759765625, 42268920643584/6525777280330657958984375, 338151365148672/815722160041332244873046875, 507227047723008/20393054001033306121826171875, 12173449145352192/8667047950439155101776123046875, 16231265527136256/216676198760978877544403076171875, 389550372651270144/102921194411464966833591461181640625, 2337302235907620864/12865149301433120854198932647705078125, 18698417887260966912/2251401127750796149484813213348388671875, 224381014647131602944/619135310131468941108323633670806884765625, 5385144351531158470656/356002803325594641137286089360713958740234375, 5385144351531158470656/8900070083139866028432152234017848968505859375, 129243464436747803295744/5562543801962416267770095146261155605316162109375, 1550921573240973639548928/1807826735637785287025280922534875571727752685546875, 1378596953991976568487936/45195668390944632175632023063371889293193817138671875, 8271581723951859410927616/7909241968415310630735604036090080626308917999267578125], [1, 49/25, 1513/625, 40129/15625, 1017049/390625, 127462901/48828125, 3187899629/1220703125, 557914285571/213623046875, 1992564670109/762939453125, 348699072073043/133514404296875, 43587387066777991/16689300537109375, 11986531516747490309/4589557647705078125, 299663288065454343293/114738941192626953125, 97390568624795071623857/37290155887603759765625, 17043349509381406454818559/6525777280330657958984375, 27667775177571609846980111/10593794286251068115234375, 53260467216825856182484436683/20393054001033306121826171875, 22635698567151001051005030942467/8667047950439155101776123046875, 565892464178775042506391300697931/216676198760978877544403076171875, 15811701204995185034122720028399257/6054187906556762754917144775390625, 33599865060614768199848082296256041989/12865149301433120854198932647705078125, 452305875815968033460931755364005254999/173184702134676626883447170257568359375, 230999072291726531374722200920137988317767/88447901447352705872617661952972412109375, 929771265974199288783262243847906934137482831/356002803325594641137286089360713958740234375, 23244281649354982219581561481342024884595541431/8900070083139866028432152234017848968505859375, 44977325172900507390831195216972848265077451053/17221497838892929621579241938889026641845703125, 39020617438225047631012435697955754709648587304443/14940716823452770967151082004420459270477294921875, 118037367750630769083812617987694754950678953164428011/45195668390944632175632023063371889293193817138671875, 20656539356360384589667208147854853698092768663185829541/7909241968415310630735604036090080626308917999267578125]]

derived = [20656539356360384589667208147854853698092768663185829541/7909241968415310630735604036090080626308917999267578125, No, finite sum is not a general infinite-value certificate]

Reverse checks

• S496 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S495 · premise_and_result_audit — Recompute Exp cumulative sum through28 with exact rational arithmetic, not rounded decimals.
• S494 · premise_and_result_audit — Recompute Exp term28 power over factorial with exact rational arithmetic, not rounded decimals.
• S493 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S492 · premise_and_result_audit — Recompute Exp term28 factorial step28 with exact rational arithmetic, not rounded decimals.
• S491 · premise_and_result_audit — Recompute Exp term28 factorial step27 with exact rational arithmetic, not rounded decimals.
• S490 · premise_and_result_audit — Recompute Exp term28 factorial step26 with exact rational arithmetic, not rounded decimals.
• S489 · premise_and_result_audit — Recompute Exp term28 factorial step25 with exact rational arithmetic, not rounded decimals.
• S488 · premise_and_result_audit — Recompute Exp term28 factorial step24 with exact rational arithmetic, not rounded decimals.
• S487 · premise_and_result_audit — Recompute Exp term28 factorial step23 with exact rational arithmetic, not rounded decimals.
• S486 · premise_and_result_audit — Recompute Exp term28 factorial step22 with exact rational arithmetic, not rounded decimals.
• S485 · premise_and_result_audit — Recompute Exp term28 factorial step21 with exact rational arithmetic, not rounded decimals.
• S484 · premise_and_result_audit — Recompute Exp term28 factorial step20 with exact rational arithmetic, not rounded decimals.
• S483 · premise_and_result_audit — Recompute Exp term28 factorial step19 with exact rational arithmetic, not rounded decimals.
• S482 · premise_and_result_audit — Recompute Exp term28 factorial step18 with exact rational arithmetic, not rounded decimals.
• S481 · premise_and_result_audit — Recompute Exp term28 factorial step17 with exact rational arithmetic, not rounded decimals.
• S480 · premise_and_result_audit — Recompute Exp term28 factorial step16 with exact rational arithmetic, not rounded decimals.
• S479 · premise_and_result_audit — Recompute Exp term28 factorial step15 with exact rational arithmetic, not rounded decimals.
• S478 · premise_and_result_audit — Recompute Exp term28 factorial step14 with exact rational arithmetic, not rounded decimals.
• S477 · premise_and_result_audit — Recompute Exp term28 factorial step13 with exact rational arithmetic, not rounded decimals.
• S476 · premise_and_result_audit — Recompute Exp term28 factorial step12 with exact rational arithmetic, not rounded decimals.
• S475 · premise_and_result_audit — Recompute Exp term28 factorial step11 with exact rational arithmetic, not rounded decimals.
• S474 · premise_and_result_audit — Recompute Exp term28 factorial step10 with exact rational arithmetic, not rounded decimals.
• S473 · premise_and_result_audit — Recompute Exp term28 factorial step9 with exact rational arithmetic, not rounded decimals.
• S472 · premise_and_result_audit — Recompute Exp term28 factorial step8 with exact rational arithmetic, not rounded decimals.
• S471 · premise_and_result_audit — Recompute Exp term28 factorial step7 with exact rational arithmetic, not rounded decimals.
• S470 · premise_and_result_audit — Recompute Exp term28 factorial step6 with exact rational arithmetic, not rounded decimals.
• S469 · premise_and_result_audit — Recompute Exp term28 factorial step5 with exact rational arithmetic, not rounded decimals.
• S468 · premise_and_result_audit — Recompute Exp term28 factorial step4 with exact rational arithmetic, not rounded decimals.
• S467 · premise_and_result_audit — Recompute Exp term28 factorial step3 with exact rational arithmetic, not rounded decimals.
• S466 · premise_and_result_audit — Recompute Exp term28 factorial step2 with exact rational arithmetic, not rounded decimals.
• S465 · premise_and_result_audit — Recompute Exp term28 factorial step1 with exact rational arithmetic, not rounded decimals.
• S464 · premise_and_result_audit — Recompute Exp cumulative sum through27 with exact rational arithmetic, not rounded decimals.
• S463 · premise_and_result_audit — Recompute Exp term27 power over factorial with exact rational arithmetic, not rounded decimals.
• S462 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S461 · premise_and_result_audit — Recompute Exp term27 factorial step27 with exact rational arithmetic, not rounded decimals.
• S460 · premise_and_result_audit — Recompute Exp term27 factorial step26 with exact rational arithmetic, not rounded decimals.
• S459 · premise_and_result_audit — Recompute Exp term27 factorial step25 with exact rational arithmetic, not rounded decimals.
• S458 · premise_and_result_audit — Recompute Exp term27 factorial step24 with exact rational arithmetic, not rounded decimals.
• S457 · premise_and_result_audit — Recompute Exp term27 factorial step23 with exact rational arithmetic, not rounded decimals.
• S456 · premise_and_result_audit — Recompute Exp term27 factorial step22 with exact rational arithmetic, not rounded decimals.
• S455 · premise_and_result_audit — Recompute Exp term27 factorial step21 with exact rational arithmetic, not rounded decimals.
• S454 · premise_and_result_audit — Recompute Exp term27 factorial step20 with exact rational arithmetic, not rounded decimals.
• S453 · premise_and_result_audit — Recompute Exp term27 factorial step19 with exact rational arithmetic, not rounded decimals.
• S452 · premise_and_result_audit — Recompute Exp term27 factorial step18 with exact rational arithmetic, not rounded decimals.
• S451 · premise_and_result_audit — Recompute Exp term27 factorial step17 with exact rational arithmetic, not rounded decimals.
• S450 · premise_and_result_audit — Recompute Exp term27 factorial step16 with exact rational arithmetic, not rounded decimals.
• S449 · premise_and_result_audit — Recompute Exp term27 factorial step15 with exact rational arithmetic, not rounded decimals.
• S448 · premise_and_result_audit — Recompute Exp term27 factorial step14 with exact rational arithmetic, not rounded decimals.
• S447 · premise_and_result_audit — Recompute Exp term27 factorial step13 with exact rational arithmetic, not rounded decimals.
• S446 · premise_and_result_audit — Recompute Exp term27 factorial step12 with exact rational arithmetic, not rounded decimals.
• S445 · premise_and_result_audit — Recompute Exp term27 factorial step11 with exact rational arithmetic, not rounded decimals.
• S444 · premise_and_result_audit — Recompute Exp term27 factorial step10 with exact rational arithmetic, not rounded decimals.
• S443 · premise_and_result_audit — Recompute Exp term27 factorial step9 with exact rational arithmetic, not rounded decimals.
• S442 · premise_and_result_audit — Recompute Exp term27 factorial step8 with exact rational arithmetic, not rounded decimals.
• S441 · premise_and_result_audit — Recompute Exp term27 factorial step7 with exact rational arithmetic, not rounded decimals.
• S440 · premise_and_result_audit — Recompute Exp term27 factorial step6 with exact rational arithmetic, not rounded decimals.
• S439 · premise_and_result_audit — Recompute Exp term27 factorial step5 with exact rational arithmetic, not rounded decimals.
• S438 · premise_and_result_audit — Recompute Exp term27 factorial step4 with exact rational arithmetic, not rounded decimals.
• S437 · premise_and_result_audit — Recompute Exp term27 factorial step3 with exact rational arithmetic, not rounded decimals.
• S436 · premise_and_result_audit — Recompute Exp term27 factorial step2 with exact rational arithmetic, not rounded decimals.
• S435 · premise_and_result_audit — Recompute Exp term27 factorial step1 with exact rational arithmetic, not rounded decimals.
• S434 · premise_and_result_audit — Recompute Exp cumulative sum through26 with exact rational arithmetic, not rounded decimals.
• S433 · premise_and_result_audit — Recompute Exp term26 power over factorial with exact rational arithmetic, not rounded decimals.
• S432 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S431 · premise_and_result_audit — Recompute Exp term26 factorial step26 with exact rational arithmetic, not rounded decimals.
• S430 · premise_and_result_audit — Recompute Exp term26 factorial step25 with exact rational arithmetic, not rounded decimals.
• S429 · premise_and_result_audit — Recompute Exp term26 factorial step24 with exact rational arithmetic, not rounded decimals.
• S428 · premise_and_result_audit — Recompute Exp term26 factorial step23 with exact rational arithmetic, not rounded decimals.
• S427 · premise_and_result_audit — Recompute Exp term26 factorial step22 with exact rational arithmetic, not rounded decimals.
• S426 · premise_and_result_audit — Recompute Exp term26 factorial step21 with exact rational arithmetic, not rounded decimals.
• S425 · premise_and_result_audit — Recompute Exp term26 factorial step20 with exact rational arithmetic, not rounded decimals.
• S424 · premise_and_result_audit — Recompute Exp term26 factorial step19 with exact rational arithmetic, not rounded decimals.
• S423 · premise_and_result_audit — Recompute Exp term26 factorial step18 with exact rational arithmetic, not rounded decimals.
• S422 · premise_and_result_audit — Recompute Exp term26 factorial step17 with exact rational arithmetic, not rounded decimals.
• S421 · premise_and_result_audit — Recompute Exp term26 factorial step16 with exact rational arithmetic, not rounded decimals.
• S420 · premise_and_result_audit — Recompute Exp term26 factorial step15 with exact rational arithmetic, not rounded decimals.
• S419 · premise_and_result_audit — Recompute Exp term26 factorial step14 with exact rational arithmetic, not rounded decimals.
• S418 · premise_and_result_audit — Recompute Exp term26 factorial step13 with exact rational arithmetic, not rounded decimals.
• S417 · premise_and_result_audit — Recompute Exp term26 factorial step12 with exact rational arithmetic, not rounded decimals.
• S416 · premise_and_result_audit — Recompute Exp term26 factorial step11 with exact rational arithmetic, not rounded decimals.
• S415 · premise_and_result_audit — Recompute Exp term26 factorial step10 with exact rational arithmetic, not rounded decimals.
• S414 · premise_and_result_audit — Recompute Exp term26 factorial step9 with exact rational arithmetic, not rounded decimals.
• S413 · premise_and_result_audit — Recompute Exp term26 factorial step8 with exact rational arithmetic, not rounded decimals.
• S412 · premise_and_result_audit — Recompute Exp term26 factorial step7 with exact rational arithmetic, not rounded decimals.
• S411 · premise_and_result_audit — Recompute Exp term26 factorial step6 with exact rational arithmetic, not rounded decimals.
• S410 · premise_and_result_audit — Recompute Exp term26 factorial step5 with exact rational arithmetic, not rounded decimals.
• S409 · premise_and_result_audit — Recompute Exp term26 factorial step4 with exact rational arithmetic, not rounded decimals.
• S408 · premise_and_result_audit — Recompute Exp term26 factorial step3 with exact rational arithmetic, not rounded decimals.
• S407 · premise_and_result_audit — Recompute Exp term26 factorial step2 with exact rational arithmetic, not rounded decimals.
• S406 · premise_and_result_audit — Recompute Exp term26 factorial step1 with exact rational arithmetic, not rounded decimals.
• S405 · premise_and_result_audit — Recompute Exp cumulative sum through25 with exact rational arithmetic, not rounded decimals.
• S404 · premise_and_result_audit — Recompute Exp term25 power over factorial with exact rational arithmetic, not rounded decimals.
• S403 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S402 · premise_and_result_audit — Recompute Exp term25 factorial step25 with exact rational arithmetic, not rounded decimals.
• S401 · premise_and_result_audit — Recompute Exp term25 factorial step24 with exact rational arithmetic, not rounded decimals.
• S400 · premise_and_result_audit — Recompute Exp term25 factorial step23 with exact rational arithmetic, not rounded decimals.
• S399 · premise_and_result_audit — Recompute Exp term25 factorial step22 with exact rational arithmetic, not rounded decimals.
• S398 · premise_and_result_audit — Recompute Exp term25 factorial step21 with exact rational arithmetic, not rounded decimals.
• S397 · premise_and_result_audit — Recompute Exp term25 factorial step20 with exact rational arithmetic, not rounded decimals.
• S396 · premise_and_result_audit — Recompute Exp term25 factorial step19 with exact rational arithmetic, not rounded decimals.
• S395 · premise_and_result_audit — Recompute Exp term25 factorial step18 with exact rational arithmetic, not rounded decimals.
• S394 · premise_and_result_audit — Recompute Exp term25 factorial step17 with exact rational arithmetic, not rounded decimals.
• S393 · premise_and_result_audit — Recompute Exp term25 factorial step16 with exact rational arithmetic, not rounded decimals.
• S392 · premise_and_result_audit — Recompute Exp term25 factorial step15 with exact rational arithmetic, not rounded decimals.
• S391 · premise_and_result_audit — Recompute Exp term25 factorial step14 with exact rational arithmetic, not rounded decimals.
• S390 · premise_and_result_audit — Recompute Exp term25 factorial step13 with exact rational arithmetic, not rounded decimals.
• S389 · premise_and_result_audit — Recompute Exp term25 factorial step12 with exact rational arithmetic, not rounded decimals.
• S388 · premise_and_result_audit — Recompute Exp term25 factorial step11 with exact rational arithmetic, not rounded decimals.
• S387 · premise_and_result_audit — Recompute Exp term25 factorial step10 with exact rational arithmetic, not rounded decimals.
• S386 · premise_and_result_audit — Recompute Exp term25 factorial step9 with exact rational arithmetic, not rounded decimals.
• S385 · premise_and_result_audit — Recompute Exp term25 factorial step8 with exact rational arithmetic, not rounded decimals.
• S384 · premise_and_result_audit — Recompute Exp term25 factorial step7 with exact rational arithmetic, not rounded decimals.
• S383 · premise_and_result_audit — Recompute Exp term25 factorial step6 with exact rational arithmetic, not rounded decimals.
• S382 · premise_and_result_audit — Recompute Exp term25 factorial step5 with exact rational arithmetic, not rounded decimals.
• S381 · premise_and_result_audit — Recompute Exp term25 factorial step4 with exact rational arithmetic, not rounded decimals.
• S380 · premise_and_result_audit — Recompute Exp term25 factorial step3 with exact rational arithmetic, not rounded decimals.
• S379 · premise_and_result_audit — Recompute Exp term25 factorial step2 with exact rational arithmetic, not rounded decimals.
• S378 · premise_and_result_audit — Recompute Exp term25 factorial step1 with exact rational arithmetic, not rounded decimals.
• S377 · premise_and_result_audit — Recompute Exp cumulative sum through24 with exact rational arithmetic, not rounded decimals.
• S376 · premise_and_result_audit — Recompute Exp term24 power over factorial with exact rational arithmetic, not rounded decimals.
• S375 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S374 · premise_and_result_audit — Recompute Exp term24 factorial step24 with exact rational arithmetic, not rounded decimals.
• S373 · premise_and_result_audit — Recompute Exp term24 factorial step23 with exact rational arithmetic, not rounded decimals.
• S372 · premise_and_result_audit — Recompute Exp term24 factorial step22 with exact rational arithmetic, not rounded decimals.
• S371 · premise_and_result_audit — Recompute Exp term24 factorial step21 with exact rational arithmetic, not rounded decimals.
• S370 · premise_and_result_audit — Recompute Exp term24 factorial step20 with exact rational arithmetic, not rounded decimals.
• S369 · premise_and_result_audit — Recompute Exp term24 factorial step19 with exact rational arithmetic, not rounded decimals.
• S368 · premise_and_result_audit — Recompute Exp term24 factorial step18 with exact rational arithmetic, not rounded decimals.
• S367 · premise_and_result_audit — Recompute Exp term24 factorial step17 with exact rational arithmetic, not rounded decimals.
• S366 · premise_and_result_audit — Recompute Exp term24 factorial step16 with exact rational arithmetic, not rounded decimals.
• S365 · premise_and_result_audit — Recompute Exp term24 factorial step15 with exact rational arithmetic, not rounded decimals.
• S364 · premise_and_result_audit — Recompute Exp term24 factorial step14 with exact rational arithmetic, not rounded decimals.
• S363 · premise_and_result_audit — Recompute Exp term24 factorial step13 with exact rational arithmetic, not rounded decimals.
• S362 · premise_and_result_audit — Recompute Exp term24 factorial step12 with exact rational arithmetic, not rounded decimals.
• S361 · premise_and_result_audit — Recompute Exp term24 factorial step11 with exact rational arithmetic, not rounded decimals.
• S360 · premise_and_result_audit — Recompute Exp term24 factorial step10 with exact rational arithmetic, not rounded decimals.
• S359 · premise_and_result_audit — Recompute Exp term24 factorial step9 with exact rational arithmetic, not rounded decimals.
• S358 · premise_and_result_audit — Recompute Exp term24 factorial step8 with exact rational arithmetic, not rounded decimals.
• S357 · premise_and_result_audit — Recompute Exp term24 factorial step7 with exact rational arithmetic, not rounded decimals.
• S356 · premise_and_result_audit — Recompute Exp term24 factorial step6 with exact rational arithmetic, not rounded decimals.
• S355 · premise_and_result_audit — Recompute Exp term24 factorial step5 with exact rational arithmetic, not rounded decimals.
• S354 · premise_and_result_audit — Recompute Exp term24 factorial step4 with exact rational arithmetic, not rounded decimals.
• S353 · premise_and_result_audit — Recompute Exp term24 factorial step3 with exact rational arithmetic, not rounded decimals.
• S352 · premise_and_result_audit — Recompute Exp term24 factorial step2 with exact rational arithmetic, not rounded decimals.
• S351 · premise_and_result_audit — Recompute Exp term24 factorial step1 with exact rational arithmetic, not rounded decimals.
• S350 · premise_and_result_audit — Recompute Exp cumulative sum through23 with exact rational arithmetic, not rounded decimals.
• S349 · premise_and_result_audit — Recompute Exp term23 power over factorial with exact rational arithmetic, not rounded decimals.
• S348 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S347 · premise_and_result_audit — Recompute Exp term23 factorial step23 with exact rational arithmetic, not rounded decimals.
• S346 · premise_and_result_audit — Recompute Exp term23 factorial step22 with exact rational arithmetic, not rounded decimals.
• S345 · premise_and_result_audit — Recompute Exp term23 factorial step21 with exact rational arithmetic, not rounded decimals.
• S344 · premise_and_result_audit — Recompute Exp term23 factorial step20 with exact rational arithmetic, not rounded decimals.
• S343 · premise_and_result_audit — Recompute Exp term23 factorial step19 with exact rational arithmetic, not rounded decimals.
• S342 · premise_and_result_audit — Recompute Exp term23 factorial step18 with exact rational arithmetic, not rounded decimals.
• S341 · premise_and_result_audit — Recompute Exp term23 factorial step17 with exact rational arithmetic, not rounded decimals.
• S340 · premise_and_result_audit — Recompute Exp term23 factorial step16 with exact rational arithmetic, not rounded decimals.
• S339 · premise_and_result_audit — Recompute Exp term23 factorial step15 with exact rational arithmetic, not rounded decimals.
• S338 · premise_and_result_audit — Recompute Exp term23 factorial step14 with exact rational arithmetic, not rounded decimals.
• S337 · premise_and_result_audit — Recompute Exp term23 factorial step13 with exact rational arithmetic, not rounded decimals.
• S336 · premise_and_result_audit — Recompute Exp term23 factorial step12 with exact rational arithmetic, not rounded decimals.
• S335 · premise_and_result_audit — Recompute Exp term23 factorial step11 with exact rational arithmetic, not rounded decimals.
• S334 · premise_and_result_audit — Recompute Exp term23 factorial step10 with exact rational arithmetic, not rounded decimals.
• S333 · premise_and_result_audit — Recompute Exp term23 factorial step9 with exact rational arithmetic, not rounded decimals.
• S332 · premise_and_result_audit — Recompute Exp term23 factorial step8 with exact rational arithmetic, not rounded decimals.
• S331 · premise_and_result_audit — Recompute Exp term23 factorial step7 with exact rational arithmetic, not rounded decimals.
• S330 · premise_and_result_audit — Recompute Exp term23 factorial step6 with exact rational arithmetic, not rounded decimals.
• S329 · premise_and_result_audit — Recompute Exp term23 factorial step5 with exact rational arithmetic, not rounded decimals.
• S328 · premise_and_result_audit — Recompute Exp term23 factorial step4 with exact rational arithmetic, not rounded decimals.
• S327 · premise_and_result_audit — Recompute Exp term23 factorial step3 with exact rational arithmetic, not rounded decimals.
• S326 · premise_and_result_audit — Recompute Exp term23 factorial step2 with exact rational arithmetic, not rounded decimals.
• S325 · premise_and_result_audit — Recompute Exp term23 factorial step1 with exact rational arithmetic, not rounded decimals.
• S324 · premise_and_result_audit — Recompute Exp cumulative sum through22 with exact rational arithmetic, not rounded decimals.
• S323 · premise_and_result_audit — Recompute Exp term22 power over factorial with exact rational arithmetic, not rounded decimals.
• S322 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S321 · premise_and_result_audit — Recompute Exp term22 factorial step22 with exact rational arithmetic, not rounded decimals.
• S320 · premise_and_result_audit — Recompute Exp term22 factorial step21 with exact rational arithmetic, not rounded decimals.
• S319 · premise_and_result_audit — Recompute Exp term22 factorial step20 with exact rational arithmetic, not rounded decimals.
• S318 · premise_and_result_audit — Recompute Exp term22 factorial step19 with exact rational arithmetic, not rounded decimals.
• S317 · premise_and_result_audit — Recompute Exp term22 factorial step18 with exact rational arithmetic, not rounded decimals.
• S316 · premise_and_result_audit — Recompute Exp term22 factorial step17 with exact rational arithmetic, not rounded decimals.
• S315 · premise_and_result_audit — Recompute Exp term22 factorial step16 with exact rational arithmetic, not rounded decimals.
• S314 · premise_and_result_audit — Recompute Exp term22 factorial step15 with exact rational arithmetic, not rounded decimals.
• S313 · premise_and_result_audit — Recompute Exp term22 factorial step14 with exact rational arithmetic, not rounded decimals.
• S312 · premise_and_result_audit — Recompute Exp term22 factorial step13 with exact rational arithmetic, not rounded decimals.
• S311 · premise_and_result_audit — Recompute Exp term22 factorial step12 with exact rational arithmetic, not rounded decimals.
• S310 · premise_and_result_audit — Recompute Exp term22 factorial step11 with exact rational arithmetic, not rounded decimals.
• S309 · premise_and_result_audit — Recompute Exp term22 factorial step10 with exact rational arithmetic, not rounded decimals.
• S308 · premise_and_result_audit — Recompute Exp term22 factorial step9 with exact rational arithmetic, not rounded decimals.
• S307 · premise_and_result_audit — Recompute Exp term22 factorial step8 with exact rational arithmetic, not rounded decimals.
• S306 · premise_and_result_audit — Recompute Exp term22 factorial step7 with exact rational arithmetic, not rounded decimals.
• S305 · premise_and_result_audit — Recompute Exp term22 factorial step6 with exact rational arithmetic, not rounded decimals.
• S304 · premise_and_result_audit — Recompute Exp term22 factorial step5 with exact rational arithmetic, not rounded decimals.
• S303 · premise_and_result_audit — Recompute Exp term22 factorial step4 with exact rational arithmetic, not rounded decimals.
• S302 · premise_and_result_audit — Recompute Exp term22 factorial step3 with exact rational arithmetic, not rounded decimals.
• S301 · premise_and_result_audit — Recompute Exp term22 factorial step2 with exact rational arithmetic, not rounded decimals.
• S300 · premise_and_result_audit — Recompute Exp term22 factorial step1 with exact rational arithmetic, not rounded decimals.
• S299 · premise_and_result_audit — Recompute Exp cumulative sum through21 with exact rational arithmetic, not rounded decimals.
• S298 · premise_and_result_audit — Recompute Exp term21 power over factorial with exact rational arithmetic, not rounded decimals.
• S297 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S296 · premise_and_result_audit — Recompute Exp term21 factorial step21 with exact rational arithmetic, not rounded decimals.
• S295 · premise_and_result_audit — Recompute Exp term21 factorial step20 with exact rational arithmetic, not rounded decimals.
• S294 · premise_and_result_audit — Recompute Exp term21 factorial step19 with exact rational arithmetic, not rounded decimals.
• S293 · premise_and_result_audit — Recompute Exp term21 factorial step18 with exact rational arithmetic, not rounded decimals.
• S292 · premise_and_result_audit — Recompute Exp term21 factorial step17 with exact rational arithmetic, not rounded decimals.
• S291 · premise_and_result_audit — Recompute Exp term21 factorial step16 with exact rational arithmetic, not rounded decimals.
• S290 · premise_and_result_audit — Recompute Exp term21 factorial step15 with exact rational arithmetic, not rounded decimals.
• S289 · premise_and_result_audit — Recompute Exp term21 factorial step14 with exact rational arithmetic, not rounded decimals.
• S288 · premise_and_result_audit — Recompute Exp term21 factorial step13 with exact rational arithmetic, not rounded decimals.
• S287 · premise_and_result_audit — Recompute Exp term21 factorial step12 with exact rational arithmetic, not rounded decimals.
• S286 · premise_and_result_audit — Recompute Exp term21 factorial step11 with exact rational arithmetic, not rounded decimals.
• S285 · premise_and_result_audit — Recompute Exp term21 factorial step10 with exact rational arithmetic, not rounded decimals.
• S284 · premise_and_result_audit — Recompute Exp term21 factorial step9 with exact rational arithmetic, not rounded decimals.
• S283 · premise_and_result_audit — Recompute Exp term21 factorial step8 with exact rational arithmetic, not rounded decimals.
• S282 · premise_and_result_audit — Recompute Exp term21 factorial step7 with exact rational arithmetic, not rounded decimals.
• S281 · premise_and_result_audit — Recompute Exp term21 factorial step6 with exact rational arithmetic, not rounded decimals.
• S280 · premise_and_result_audit — Recompute Exp term21 factorial step5 with exact rational arithmetic, not rounded decimals.
• S279 · premise_and_result_audit — Recompute Exp term21 factorial step4 with exact rational arithmetic, not rounded decimals.
• S278 · premise_and_result_audit — Recompute Exp term21 factorial step3 with exact rational arithmetic, not rounded decimals.
• S277 · premise_and_result_audit — Recompute Exp term21 factorial step2 with exact rational arithmetic, not rounded decimals.
• S276 · premise_and_result_audit — Recompute Exp term21 factorial step1 with exact rational arithmetic, not rounded decimals.
• S275 · premise_and_result_audit — Recompute Exp cumulative sum through20 with exact rational arithmetic, not rounded decimals.
• S274 · premise_and_result_audit — Recompute Exp term20 power over factorial with exact rational arithmetic, not rounded decimals.
• S273 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S272 · premise_and_result_audit — Recompute Exp term20 factorial step20 with exact rational arithmetic, not rounded decimals.
• S271 · premise_and_result_audit — Recompute Exp term20 factorial step19 with exact rational arithmetic, not rounded decimals.
• S270 · premise_and_result_audit — Recompute Exp term20 factorial step18 with exact rational arithmetic, not rounded decimals.
• S269 · premise_and_result_audit — Recompute Exp term20 factorial step17 with exact rational arithmetic, not rounded decimals.
• S268 · premise_and_result_audit — Recompute Exp term20 factorial step16 with exact rational arithmetic, not rounded decimals.
• S267 · premise_and_result_audit — Recompute Exp term20 factorial step15 with exact rational arithmetic, not rounded decimals.
• S266 · premise_and_result_audit — Recompute Exp term20 factorial step14 with exact rational arithmetic, not rounded decimals.
• S265 · premise_and_result_audit — Recompute Exp term20 factorial step13 with exact rational arithmetic, not rounded decimals.
• S264 · premise_and_result_audit — Recompute Exp term20 factorial step12 with exact rational arithmetic, not rounded decimals.
• S263 · premise_and_result_audit — Recompute Exp term20 factorial step11 with exact rational arithmetic, not rounded decimals.
• S262 · premise_and_result_audit — Recompute Exp term20 factorial step10 with exact rational arithmetic, not rounded decimals.
• S261 · premise_and_result_audit — Recompute Exp term20 factorial step9 with exact rational arithmetic, not rounded decimals.
• S260 · premise_and_result_audit — Recompute Exp term20 factorial step8 with exact rational arithmetic, not rounded decimals.
• S259 · premise_and_result_audit — Recompute Exp term20 factorial step7 with exact rational arithmetic, not rounded decimals.
• S258 · premise_and_result_audit — Recompute Exp term20 factorial step6 with exact rational arithmetic, not rounded decimals.
• S257 · premise_and_result_audit — Recompute Exp term20 factorial step5 with exact rational arithmetic, not rounded decimals.
• S256 · premise_and_result_audit — Recompute Exp term20 factorial step4 with exact rational arithmetic, not rounded decimals.
• S255 · premise_and_result_audit — Recompute Exp term20 factorial step3 with exact rational arithmetic, not rounded decimals.
• S254 · premise_and_result_audit — Recompute Exp term20 factorial step2 with exact rational arithmetic, not rounded decimals.
• S253 · premise_and_result_audit — Recompute Exp term20 factorial step1 with exact rational arithmetic, not rounded decimals.
• S252 · premise_and_result_audit — Recompute Exp cumulative sum through19 with exact rational arithmetic, not rounded decimals.
• S251 · premise_and_result_audit — Recompute Exp term19 power over factorial with exact rational arithmetic, not rounded decimals.
• S250 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S249 · premise_and_result_audit — Recompute Exp term19 factorial step19 with exact rational arithmetic, not rounded decimals.
• S248 · premise_and_result_audit — Recompute Exp term19 factorial step18 with exact rational arithmetic, not rounded decimals.
• S247 · premise_and_result_audit — Recompute Exp term19 factorial step17 with exact rational arithmetic, not rounded decimals.
• S246 · premise_and_result_audit — Recompute Exp term19 factorial step16 with exact rational arithmetic, not rounded decimals.
• S245 · premise_and_result_audit — Recompute Exp term19 factorial step15 with exact rational arithmetic, not rounded decimals.
• S244 · premise_and_result_audit — Recompute Exp term19 factorial step14 with exact rational arithmetic, not rounded decimals.
• S243 · premise_and_result_audit — Recompute Exp term19 factorial step13 with exact rational arithmetic, not rounded decimals.
• S242 · premise_and_result_audit — Recompute Exp term19 factorial step12 with exact rational arithmetic, not rounded decimals.
• S241 · premise_and_result_audit — Recompute Exp term19 factorial step11 with exact rational arithmetic, not rounded decimals.
• S240 · premise_and_result_audit — Recompute Exp term19 factorial step10 with exact rational arithmetic, not rounded decimals.
• S239 · premise_and_result_audit — Recompute Exp term19 factorial step9 with exact rational arithmetic, not rounded decimals.
• S238 · premise_and_result_audit — Recompute Exp term19 factorial step8 with exact rational arithmetic, not rounded decimals.
• S237 · premise_and_result_audit — Recompute Exp term19 factorial step7 with exact rational arithmetic, not rounded decimals.
• S236 · premise_and_result_audit — Recompute Exp term19 factorial step6 with exact rational arithmetic, not rounded decimals.
• S235 · premise_and_result_audit — Recompute Exp term19 factorial step5 with exact rational arithmetic, not rounded decimals.
• S234 · premise_and_result_audit — Recompute Exp term19 factorial step4 with exact rational arithmetic, not rounded decimals.
• S233 · premise_and_result_audit — Recompute Exp term19 factorial step3 with exact rational arithmetic, not rounded decimals.
• S232 · premise_and_result_audit — Recompute Exp term19 factorial step2 with exact rational arithmetic, not rounded decimals.
• S231 · premise_and_result_audit — Recompute Exp term19 factorial step1 with exact rational arithmetic, not rounded decimals.
• S230 · premise_and_result_audit — Recompute Exp cumulative sum through18 with exact rational arithmetic, not rounded decimals.
• S229 · premise_and_result_audit — Recompute Exp term18 power over factorial with exact rational arithmetic, not rounded decimals.
• S228 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S227 · premise_and_result_audit — Recompute Exp term18 factorial step18 with exact rational arithmetic, not rounded decimals.
• S226 · premise_and_result_audit — Recompute Exp term18 factorial step17 with exact rational arithmetic, not rounded decimals.
• S225 · premise_and_result_audit — Recompute Exp term18 factorial step16 with exact rational arithmetic, not rounded decimals.
• S224 · premise_and_result_audit — Recompute Exp term18 factorial step15 with exact rational arithmetic, not rounded decimals.
• S223 · premise_and_result_audit — Recompute Exp term18 factorial step14 with exact rational arithmetic, not rounded decimals.
• S222 · premise_and_result_audit — Recompute Exp term18 factorial step13 with exact rational arithmetic, not rounded decimals.
• S221 · premise_and_result_audit — Recompute Exp term18 factorial step12 with exact rational arithmetic, not rounded decimals.
• S220 · premise_and_result_audit — Recompute Exp term18 factorial step11 with exact rational arithmetic, not rounded decimals.
• S219 · premise_and_result_audit — Recompute Exp term18 factorial step10 with exact rational arithmetic, not rounded decimals.
• S218 · premise_and_result_audit — Recompute Exp term18 factorial step9 with exact rational arithmetic, not rounded decimals.
• S217 · premise_and_result_audit — Recompute Exp term18 factorial step8 with exact rational arithmetic, not rounded decimals.
• S216 · premise_and_result_audit — Recompute Exp term18 factorial step7 with exact rational arithmetic, not rounded decimals.
• S215 · premise_and_result_audit — Recompute Exp term18 factorial step6 with exact rational arithmetic, not rounded decimals.
• S214 · premise_and_result_audit — Recompute Exp term18 factorial step5 with exact rational arithmetic, not rounded decimals.
• S213 · premise_and_result_audit — Recompute Exp term18 factorial step4 with exact rational arithmetic, not rounded decimals.
• S212 · premise_and_result_audit — Recompute Exp term18 factorial step3 with exact rational arithmetic, not rounded decimals.
• S211 · premise_and_result_audit — Recompute Exp term18 factorial step2 with exact rational arithmetic, not rounded decimals.
• S210 · premise_and_result_audit — Recompute Exp term18 factorial step1 with exact rational arithmetic, not rounded decimals.
• S209 · premise_and_result_audit — Recompute Exp cumulative sum through17 with exact rational arithmetic, not rounded decimals.
• S208 · premise_and_result_audit — Recompute Exp term17 power over factorial with exact rational arithmetic, not rounded decimals.
• S207 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S206 · premise_and_result_audit — Recompute Exp term17 factorial step17 with exact rational arithmetic, not rounded decimals.
• S205 · premise_and_result_audit — Recompute Exp term17 factorial step16 with exact rational arithmetic, not rounded decimals.
• S204 · premise_and_result_audit — Recompute Exp term17 factorial step15 with exact rational arithmetic, not rounded decimals.
• S203 · premise_and_result_audit — Recompute Exp term17 factorial step14 with exact rational arithmetic, not rounded decimals.
• S202 · premise_and_result_audit — Recompute Exp term17 factorial step13 with exact rational arithmetic, not rounded decimals.
• S201 · premise_and_result_audit — Recompute Exp term17 factorial step12 with exact rational arithmetic, not rounded decimals.
• S200 · premise_and_result_audit — Recompute Exp term17 factorial step11 with exact rational arithmetic, not rounded decimals.
• S199 · premise_and_result_audit — Recompute Exp term17 factorial step10 with exact rational arithmetic, not rounded decimals.
• S198 · premise_and_result_audit — Recompute Exp term17 factorial step9 with exact rational arithmetic, not rounded decimals.
• S197 · premise_and_result_audit — Recompute Exp term17 factorial step8 with exact rational arithmetic, not rounded decimals.
• S196 · premise_and_result_audit — Recompute Exp term17 factorial step7 with exact rational arithmetic, not rounded decimals.
• S195 · premise_and_result_audit — Recompute Exp term17 factorial step6 with exact rational arithmetic, not rounded decimals.
• S194 · premise_and_result_audit — Recompute Exp term17 factorial step5 with exact rational arithmetic, not rounded decimals.
• S193 · premise_and_result_audit — Recompute Exp term17 factorial step4 with exact rational arithmetic, not rounded decimals.
• S192 · premise_and_result_audit — Recompute Exp term17 factorial step3 with exact rational arithmetic, not rounded decimals.
• S191 · premise_and_result_audit — Recompute Exp term17 factorial step2 with exact rational arithmetic, not rounded decimals.
• S190 · premise_and_result_audit — Recompute Exp term17 factorial step1 with exact rational arithmetic, not rounded decimals.
• S189 · premise_and_result_audit — Recompute Exp cumulative sum through16 with exact rational arithmetic, not rounded decimals.
• S188 · premise_and_result_audit — Recompute Exp term16 power over factorial with exact rational arithmetic, not rounded decimals.
• S187 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S186 · premise_and_result_audit — Recompute Exp term16 factorial step16 with exact rational arithmetic, not rounded decimals.
• S185 · premise_and_result_audit — Recompute Exp term16 factorial step15 with exact rational arithmetic, not rounded decimals.
• S184 · premise_and_result_audit — Recompute Exp term16 factorial step14 with exact rational arithmetic, not rounded decimals.
• S183 · premise_and_result_audit — Recompute Exp term16 factorial step13 with exact rational arithmetic, not rounded decimals.
• S182 · premise_and_result_audit — Recompute Exp term16 factorial step12 with exact rational arithmetic, not rounded decimals.
• S181 · premise_and_result_audit — Recompute Exp term16 factorial step11 with exact rational arithmetic, not rounded decimals.
• S180 · premise_and_result_audit — Recompute Exp term16 factorial step10 with exact rational arithmetic, not rounded decimals.
• S179 · premise_and_result_audit — Recompute Exp term16 factorial step9 with exact rational arithmetic, not rounded decimals.
• S178 · premise_and_result_audit — Recompute Exp term16 factorial step8 with exact rational arithmetic, not rounded decimals.
• S177 · premise_and_result_audit — Recompute Exp term16 factorial step7 with exact rational arithmetic, not rounded decimals.
• S176 · premise_and_result_audit — Recompute Exp term16 factorial step6 with exact rational arithmetic, not rounded decimals.
• S175 · premise_and_result_audit — Recompute Exp term16 factorial step5 with exact rational arithmetic, not rounded decimals.
• S174 · premise_and_result_audit — Recompute Exp term16 factorial step4 with exact rational arithmetic, not rounded decimals.
• S173 · premise_and_result_audit — Recompute Exp term16 factorial step3 with exact rational arithmetic, not rounded decimals.
• S172 · premise_and_result_audit — Recompute Exp term16 factorial step2 with exact rational arithmetic, not rounded decimals.
• S171 · premise_and_result_audit — Recompute Exp term16 factorial step1 with exact rational arithmetic, not rounded decimals.
• S170 · premise_and_result_audit — Recompute Exp cumulative sum through15 with exact rational arithmetic, not rounded decimals.
• S169 · premise_and_result_audit — Recompute Exp term15 power over factorial with exact rational arithmetic, not rounded decimals.
• S168 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S167 · premise_and_result_audit — Recompute Exp term15 factorial step15 with exact rational arithmetic, not rounded decimals.
• S166 · premise_and_result_audit — Recompute Exp term15 factorial step14 with exact rational arithmetic, not rounded decimals.
• S165 · premise_and_result_audit — Recompute Exp term15 factorial step13 with exact rational arithmetic, not rounded decimals.
• S164 · premise_and_result_audit — Recompute Exp term15 factorial step12 with exact rational arithmetic, not rounded decimals.
• S163 · premise_and_result_audit — Recompute Exp term15 factorial step11 with exact rational arithmetic, not rounded decimals.
• S162 · premise_and_result_audit — Recompute Exp term15 factorial step10 with exact rational arithmetic, not rounded decimals.
• S161 · premise_and_result_audit — Recompute Exp term15 factorial step9 with exact rational arithmetic, not rounded decimals.
• S160 · premise_and_result_audit — Recompute Exp term15 factorial step8 with exact rational arithmetic, not rounded decimals.
• S159 · premise_and_result_audit — Recompute Exp term15 factorial step7 with exact rational arithmetic, not rounded decimals.
• S158 · premise_and_result_audit — Recompute Exp term15 factorial step6 with exact rational arithmetic, not rounded decimals.
• S157 · premise_and_result_audit — Recompute Exp term15 factorial step5 with exact rational arithmetic, not rounded decimals.
• S156 · premise_and_result_audit — Recompute Exp term15 factorial step4 with exact rational arithmetic, not rounded decimals.
• S155 · premise_and_result_audit — Recompute Exp term15 factorial step3 with exact rational arithmetic, not rounded decimals.
• S154 · premise_and_result_audit — Recompute Exp term15 factorial step2 with exact rational arithmetic, not rounded decimals.
• S153 · premise_and_result_audit — Recompute Exp term15 factorial step1 with exact rational arithmetic, not rounded decimals.
• S152 · premise_and_result_audit — Recompute Exp cumulative sum through14 with exact rational arithmetic, not rounded decimals.
• S151 · premise_and_result_audit — Recompute Exp term14 power over factorial with exact rational arithmetic, not rounded decimals.
• S150 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S149 · premise_and_result_audit — Recompute Exp term14 factorial step14 with exact rational arithmetic, not rounded decimals.
• S148 · premise_and_result_audit — Recompute Exp term14 factorial step13 with exact rational arithmetic, not rounded decimals.
• S147 · premise_and_result_audit — Recompute Exp term14 factorial step12 with exact rational arithmetic, not rounded decimals.
• S146 · premise_and_result_audit — Recompute Exp term14 factorial step11 with exact rational arithmetic, not rounded decimals.
• S145 · premise_and_result_audit — Recompute Exp term14 factorial step10 with exact rational arithmetic, not rounded decimals.
• S144 · premise_and_result_audit — Recompute Exp term14 factorial step9 with exact rational arithmetic, not rounded decimals.
• S143 · premise_and_result_audit — Recompute Exp term14 factorial step8 with exact rational arithmetic, not rounded decimals.
• S142 · premise_and_result_audit — Recompute Exp term14 factorial step7 with exact rational arithmetic, not rounded decimals.
• S141 · premise_and_result_audit — Recompute Exp term14 factorial step6 with exact rational arithmetic, not rounded decimals.
• S140 · premise_and_result_audit — Recompute Exp term14 factorial step5 with exact rational arithmetic, not rounded decimals.
• S139 · premise_and_result_audit — Recompute Exp term14 factorial step4 with exact rational arithmetic, not rounded decimals.
• S138 · premise_and_result_audit — Recompute Exp term14 factorial step3 with exact rational arithmetic, not rounded decimals.
• S137 · premise_and_result_audit — Recompute Exp term14 factorial step2 with exact rational arithmetic, not rounded decimals.
• S136 · premise_and_result_audit — Recompute Exp term14 factorial step1 with exact rational arithmetic, not rounded decimals.
• S135 · premise_and_result_audit — Recompute Exp cumulative sum through13 with exact rational arithmetic, not rounded decimals.
• S134 · premise_and_result_audit — Recompute Exp term13 power over factorial with exact rational arithmetic, not rounded decimals.
• S133 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S132 · premise_and_result_audit — Recompute Exp term13 factorial step13 with exact rational arithmetic, not rounded decimals.
• S131 · premise_and_result_audit — Recompute Exp term13 factorial step12 with exact rational arithmetic, not rounded decimals.
• S130 · premise_and_result_audit — Recompute Exp term13 factorial step11 with exact rational arithmetic, not rounded decimals.
• S129 · premise_and_result_audit — Recompute Exp term13 factorial step10 with exact rational arithmetic, not rounded decimals.
• S128 · premise_and_result_audit — Recompute Exp term13 factorial step9 with exact rational arithmetic, not rounded decimals.
• S127 · premise_and_result_audit — Recompute Exp term13 factorial step8 with exact rational arithmetic, not rounded decimals.
• S126 · premise_and_result_audit — Recompute Exp term13 factorial step7 with exact rational arithmetic, not rounded decimals.
• S125 · premise_and_result_audit — Recompute Exp term13 factorial step6 with exact rational arithmetic, not rounded decimals.
• S124 · premise_and_result_audit — Recompute Exp term13 factorial step5 with exact rational arithmetic, not rounded decimals.
• S123 · premise_and_result_audit — Recompute Exp term13 factorial step4 with exact rational arithmetic, not rounded decimals.
• S122 · premise_and_result_audit — Recompute Exp term13 factorial step3 with exact rational arithmetic, not rounded decimals.
• S121 · premise_and_result_audit — Recompute Exp term13 factorial step2 with exact rational arithmetic, not rounded decimals.
• S120 · premise_and_result_audit — Recompute Exp term13 factorial step1 with exact rational arithmetic, not rounded decimals.
• S119 · premise_and_result_audit — Recompute Exp cumulative sum through12 with exact rational arithmetic, not rounded decimals.
• S118 · premise_and_result_audit — Recompute Exp term12 power over factorial with exact rational arithmetic, not rounded decimals.
• S117 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S116 · premise_and_result_audit — Recompute Exp term12 factorial step12 with exact rational arithmetic, not rounded decimals.
• S115 · premise_and_result_audit — Recompute Exp term12 factorial step11 with exact rational arithmetic, not rounded decimals.
• S114 · premise_and_result_audit — Recompute Exp term12 factorial step10 with exact rational arithmetic, not rounded decimals.
• S113 · premise_and_result_audit — Recompute Exp term12 factorial step9 with exact rational arithmetic, not rounded decimals.
• S112 · premise_and_result_audit — Recompute Exp term12 factorial step8 with exact rational arithmetic, not rounded decimals.
• S111 · premise_and_result_audit — Recompute Exp term12 factorial step7 with exact rational arithmetic, not rounded decimals.
• S110 · premise_and_result_audit — Recompute Exp term12 factorial step6 with exact rational arithmetic, not rounded decimals.
• S109 · premise_and_result_audit — Recompute Exp term12 factorial step5 with exact rational arithmetic, not rounded decimals.
• S108 · premise_and_result_audit — Recompute Exp term12 factorial step4 with exact rational arithmetic, not rounded decimals.
• S107 · premise_and_result_audit — Recompute Exp term12 factorial step3 with exact rational arithmetic, not rounded decimals.
• S106 · premise_and_result_audit — Recompute Exp term12 factorial step2 with exact rational arithmetic, not rounded decimals.
• S105 · premise_and_result_audit — Recompute Exp term12 factorial step1 with exact rational arithmetic, not rounded decimals.
• S104 · premise_and_result_audit — Recompute Exp cumulative sum through11 with exact rational arithmetic, not rounded decimals.
• S103 · premise_and_result_audit — Recompute Exp term11 power over factorial with exact rational arithmetic, not rounded decimals.
• S102 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S101 · premise_and_result_audit — Recompute Exp term11 factorial step11 with exact rational arithmetic, not rounded decimals.
• S100 · premise_and_result_audit — Recompute Exp term11 factorial step10 with exact rational arithmetic, not rounded decimals.
• S099 · premise_and_result_audit — Recompute Exp term11 factorial step9 with exact rational arithmetic, not rounded decimals.
• S098 · premise_and_result_audit — Recompute Exp term11 factorial step8 with exact rational arithmetic, not rounded decimals.
• S097 · premise_and_result_audit — Recompute Exp term11 factorial step7 with exact rational arithmetic, not rounded decimals.
• S096 · premise_and_result_audit — Recompute Exp term11 factorial step6 with exact rational arithmetic, not rounded decimals.
• S095 · premise_and_result_audit — Recompute Exp term11 factorial step5 with exact rational arithmetic, not rounded decimals.
• S094 · premise_and_result_audit — Recompute Exp term11 factorial step4 with exact rational arithmetic, not rounded decimals.
• S093 · premise_and_result_audit — Recompute Exp term11 factorial step3 with exact rational arithmetic, not rounded decimals.
• S092 · premise_and_result_audit — Recompute Exp term11 factorial step2 with exact rational arithmetic, not rounded decimals.
• S091 · premise_and_result_audit — Recompute Exp term11 factorial step1 with exact rational arithmetic, not rounded decimals.
• S090 · premise_and_result_audit — Recompute Exp cumulative sum through10 with exact rational arithmetic, not rounded decimals.
• S089 · premise_and_result_audit — Recompute Exp term10 power over factorial with exact rational arithmetic, not rounded decimals.
• S088 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S087 · premise_and_result_audit — Recompute Exp term10 factorial step10 with exact rational arithmetic, not rounded decimals.
• S086 · premise_and_result_audit — Recompute Exp term10 factorial step9 with exact rational arithmetic, not rounded decimals.
• S085 · premise_and_result_audit — Recompute Exp term10 factorial step8 with exact rational arithmetic, not rounded decimals.
• S084 · premise_and_result_audit — Recompute Exp term10 factorial step7 with exact rational arithmetic, not rounded decimals.
• S083 · premise_and_result_audit — Recompute Exp term10 factorial step6 with exact rational arithmetic, not rounded decimals.
• S082 · premise_and_result_audit — Recompute Exp term10 factorial step5 with exact rational arithmetic, not rounded decimals.
• S081 · premise_and_result_audit — Recompute Exp term10 factorial step4 with exact rational arithmetic, not rounded decimals.
• S080 · premise_and_result_audit — Recompute Exp term10 factorial step3 with exact rational arithmetic, not rounded decimals.
• S079 · premise_and_result_audit — Recompute Exp term10 factorial step2 with exact rational arithmetic, not rounded decimals.
• S078 · premise_and_result_audit — Recompute Exp term10 factorial step1 with exact rational arithmetic, not rounded decimals.
• S077 · premise_and_result_audit — Recompute Exp cumulative sum through9 with exact rational arithmetic, not rounded decimals.
• S076 · premise_and_result_audit — Recompute Exp term9 power over factorial with exact rational arithmetic, not rounded decimals.
• S075 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S074 · premise_and_result_audit — Recompute Exp term9 factorial step9 with exact rational arithmetic, not rounded decimals.
• S073 · premise_and_result_audit — Recompute Exp term9 factorial step8 with exact rational arithmetic, not rounded decimals.
• S072 · premise_and_result_audit — Recompute Exp term9 factorial step7 with exact rational arithmetic, not rounded decimals.
• S071 · premise_and_result_audit — Recompute Exp term9 factorial step6 with exact rational arithmetic, not rounded decimals.
• S070 · premise_and_result_audit — Recompute Exp term9 factorial step5 with exact rational arithmetic, not rounded decimals.
• S069 · premise_and_result_audit — Recompute Exp term9 factorial step4 with exact rational arithmetic, not rounded decimals.
• S068 · premise_and_result_audit — Recompute Exp term9 factorial step3 with exact rational arithmetic, not rounded decimals.
• S067 · premise_and_result_audit — Recompute Exp term9 factorial step2 with exact rational arithmetic, not rounded decimals.
• S066 · premise_and_result_audit — Recompute Exp term9 factorial step1 with exact rational arithmetic, not rounded decimals.
• S065 · premise_and_result_audit — Recompute Exp cumulative sum through8 with exact rational arithmetic, not rounded decimals.
• S064 · premise_and_result_audit — Recompute Exp term8 power over factorial with exact rational arithmetic, not rounded decimals.
• S063 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S062 · premise_and_result_audit — Recompute Exp term8 factorial step8 with exact rational arithmetic, not rounded decimals.
• S061 · premise_and_result_audit — Recompute Exp term8 factorial step7 with exact rational arithmetic, not rounded decimals.
• S060 · premise_and_result_audit — Recompute Exp term8 factorial step6 with exact rational arithmetic, not rounded decimals.
• S059 · premise_and_result_audit — Recompute Exp term8 factorial step5 with exact rational arithmetic, not rounded decimals.
• S058 · premise_and_result_audit — Recompute Exp term8 factorial step4 with exact rational arithmetic, not rounded decimals.
• S057 · premise_and_result_audit — Recompute Exp term8 factorial step3 with exact rational arithmetic, not rounded decimals.
• S056 · premise_and_result_audit — Recompute Exp term8 factorial step2 with exact rational arithmetic, not rounded decimals.
• S055 · premise_and_result_audit — Recompute Exp term8 factorial step1 with exact rational arithmetic, not rounded decimals.
• S054 · premise_and_result_audit — Recompute Exp cumulative sum through7 with exact rational arithmetic, not rounded decimals.
• S053 · premise_and_result_audit — Recompute Exp term7 power over factorial with exact rational arithmetic, not rounded decimals.
• S052 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S051 · premise_and_result_audit — Recompute Exp term7 factorial step7 with exact rational arithmetic, not rounded decimals.
• S050 · premise_and_result_audit — Recompute Exp term7 factorial step6 with exact rational arithmetic, not rounded decimals.
• S049 · premise_and_result_audit — Recompute Exp term7 factorial step5 with exact rational arithmetic, not rounded decimals.
• S048 · premise_and_result_audit — Recompute Exp term7 factorial step4 with exact rational arithmetic, not rounded decimals.
• S047 · premise_and_result_audit — Recompute Exp term7 factorial step3 with exact rational arithmetic, not rounded decimals.
• S046 · premise_and_result_audit — Recompute Exp term7 factorial step2 with exact rational arithmetic, not rounded decimals.
• S045 · premise_and_result_audit — Recompute Exp term7 factorial step1 with exact rational arithmetic, not rounded decimals.
• S044 · premise_and_result_audit — Recompute Exp cumulative sum through6 with exact rational arithmetic, not rounded decimals.
• S043 · premise_and_result_audit — Recompute Exp term6 power over factorial with exact rational arithmetic, not rounded decimals.
• S042 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S041 · premise_and_result_audit — Recompute Exp term6 factorial step6 with exact rational arithmetic, not rounded decimals.
• S040 · premise_and_result_audit — Recompute Exp term6 factorial step5 with exact rational arithmetic, not rounded decimals.
• S039 · premise_and_result_audit — Recompute Exp term6 factorial step4 with exact rational arithmetic, not rounded decimals.
• S038 · premise_and_result_audit — Recompute Exp term6 factorial step3 with exact rational arithmetic, not rounded decimals.
• S037 · premise_and_result_audit — Recompute Exp term6 factorial step2 with exact rational arithmetic, not rounded decimals.
• S036 · premise_and_result_audit — Recompute Exp term6 factorial step1 with exact rational arithmetic, not rounded decimals.
• S035 · premise_and_result_audit — Recompute Exp cumulative sum through5 with exact rational arithmetic, not rounded decimals.
• S034 · premise_and_result_audit — Recompute Exp term5 power over factorial with exact rational arithmetic, not rounded decimals.
• S033 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S032 · premise_and_result_audit — Recompute Exp term5 factorial step5 with exact rational arithmetic, not rounded decimals.
• S031 · premise_and_result_audit — Recompute Exp term5 factorial step4 with exact rational arithmetic, not rounded decimals.
• S030 · premise_and_result_audit — Recompute Exp term5 factorial step3 with exact rational arithmetic, not rounded decimals.
• S029 · premise_and_result_audit — Recompute Exp term5 factorial step2 with exact rational arithmetic, not rounded decimals.
• S028 · premise_and_result_audit — Recompute Exp term5 factorial step1 with exact rational arithmetic, not rounded decimals.
• S027 · premise_and_result_audit — Recompute Exp cumulative sum through4 with exact rational arithmetic, not rounded decimals.
• S026 · premise_and_result_audit — Recompute Exp term4 power over factorial with exact rational arithmetic, not rounded decimals.
• S025 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S024 · premise_and_result_audit — Recompute Exp term4 factorial step4 with exact rational arithmetic, not rounded decimals.
• S023 · premise_and_result_audit — Recompute Exp term4 factorial step3 with exact rational arithmetic, not rounded decimals.
• S022 · premise_and_result_audit — Recompute Exp term4 factorial step2 with exact rational arithmetic, not rounded decimals.
• S021 · premise_and_result_audit — Recompute Exp term4 factorial step1 with exact rational arithmetic, not rounded decimals.
• S020 · premise_and_result_audit — Recompute Exp cumulative sum through3 with exact rational arithmetic, not rounded decimals.
• S019 · premise_and_result_audit — Recompute Exp term3 power over factorial with exact rational arithmetic, not rounded decimals.
• S018 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S017 · premise_and_result_audit — Recompute Exp term3 factorial step3 with exact rational arithmetic, not rounded decimals.
• S016 · premise_and_result_audit — Recompute Exp term3 factorial step2 with exact rational arithmetic, not rounded decimals.
• S015 · premise_and_result_audit — Recompute Exp term3 factorial step1 with exact rational arithmetic, not rounded decimals.
• S014 · premise_and_result_audit — Recompute Exp cumulative sum through2 with exact rational arithmetic, not rounded decimals.
• S013 · premise_and_result_audit — Recompute Exp term2 power over factorial with exact rational arithmetic, not rounded decimals.
• S012 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S011 · premise_and_result_audit — Recompute Exp term2 factorial step2 with exact rational arithmetic, not rounded decimals.
• S010 · premise_and_result_audit — Recompute Exp term2 factorial step1 with exact rational arithmetic, not rounded decimals.
• S009 · premise_and_result_audit — Recompute Exp cumulative sum through1 with exact rational arithmetic, not rounded decimals.
• S008 · premise_and_result_audit — Recompute Exp term1 power over factorial with exact rational arithmetic, not rounded decimals.
• S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S006 · premise_and_result_audit — Recompute Exp term1 factorial step1 with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Recompute Exp cumulative sum through0 with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Recompute Exp term0 power over factorial with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(24/25, 28, [1, 24/25, 288/625, 2304/15625, 13824/390625, 331776/48828125, 1327104/1220703125, 31850496/213623046875, 95551488/5340576171875, 254803968/133514404296875, 3057647616/16689300537109375, 73383542784/4589557647705078125, 146767085568/114738941192626953125, 3522410053632/37290155887603759765625, 42268920643584/6525777280330657958984375, 338151365148672/815722160041332244873046875, 507227047723008/20393054001033306121826171875, 12173449145352192/8667047950439155101776123046875, 16231265527136256/216676198760978877544403076171875, 389550372651270144/102921194411464966833591461181640625, 2337302235907620864/12865149301433120854198932647705078125, 18698417887260966912/2251401127750796149484813213348388671875, 224381014647131602944/619135310131468941108323633670806884765625, 5385144351531158470656/356002803325594641137286089360713958740234375, 5385144351531158470656/8900070083139866028432152234017848968505859375, 129243464436747803295744/5562543801962416267770095146261155605316162109375, 1550921573240973639548928/1807826735637785287025280922534875571727752685546875, 1378596953991976568487936/45195668390944632175632023063371889293193817138671875, 8271581723951859410927616/7909241968415310630735604036090080626308917999267578125], [1, 49/25, 1513/625, 40129/15625, 1017049/390625, 127462901/48828125, 3187899629/1220703125, 557914285571/213623046875, 1992564670109/762939453125, 348699072073043/133514404296875, 43587387066777991/16689300537109375, 11986531516747490309/4589557647705078125, 299663288065454343293/114738941192626953125, 97390568624795071623857/37290155887603759765625, 17043349509381406454818559/6525777280330657958984375, 27667775177571609846980111/10593794286251068115234375, 53260467216825856182484436683/20393054001033306121826171875, 22635698567151001051005030942467/8667047950439155101776123046875, 565892464178775042506391300697931/216676198760978877544403076171875, 15811701204995185034122720028399257/6054187906556762754917144775390625, 33599865060614768199848082296256041989/12865149301433120854198932647705078125, 452305875815968033460931755364005254999/173184702134676626883447170257568359375, 230999072291726531374722200920137988317767/88447901447352705872617661952972412109375, 929771265974199288783262243847906934137482831/356002803325594641137286089360713958740234375, 23244281649354982219581561481342024884595541431/8900070083139866028432152234017848968505859375, 44977325172900507390831195216972848265077451053/17221497838892929621579241938889026641845703125, 39020617438225047631012435697955754709648587304443/14940716823452770967151082004420459270477294921875, 118037367750630769083812617987694754950678953164428011/45195668390944632175632023063371889293193817138671875, 20656539356360384589667208147854853698092768663185829541/7909241968415310630735604036090080626308917999267578125], 20656539356360384589667208147854853698092768663185829541/7909241968415310630735604036090080626308917999267578125, No, finite_partial_sum_is_not_the_infinite_exponential_value)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.