Question 24248: 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=23/24, cutoff=27, 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=23/24, cutoff=27, 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]

(23/24)^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

(23/24)^1

Exp ORIGINAL x power1 = 23/24

Exp term1 power over factorial := div(23/24, 1)

Exp term1 power over factorial = 23/24

Exp cumulative sum through1 := sum(1, 23/24)

Exp cumulative sum through1 = 47/24

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

Exp term2 factorial step1 = 1

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

Exp term2 factorial step2 = 2

(23/24)^2

Exp ORIGINAL x power2 = 529/576

Exp term2 power over factorial := div(529/576, 2)

Exp term2 power over factorial = 529/1152

Exp cumulative sum through2 := sum(47/24, 529/1152)

Exp cumulative sum through2 = 2785/1152

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

(23/24)^3

Exp ORIGINAL x power3 = 12167/13824

Exp term3 power over factorial := div(12167/13824, 6)

Exp term3 power over factorial = 12167/82944

Exp cumulative sum through3 := sum(2785/1152, 12167/82944)

Exp cumulative sum through3 = 212687/82944

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

(23/24)^4

Exp ORIGINAL x power4 = 279841/331776

Exp term4 power over factorial := div(279841/331776, 24)

Exp term4 power over factorial = 279841/7962624

Exp cumulative sum through4 := sum(212687/82944, 279841/7962624)

Exp cumulative sum through4 = 20697793/7962624

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

(23/24)^5

Exp ORIGINAL x power5 = 6436343/7962624

Exp term5 power over factorial := div(6436343/7962624, 120)

Exp term5 power over factorial = 6436343/955514880

Exp cumulative sum through5 := sum(20697793/7962624, 6436343/955514880)

Exp cumulative sum through5 = 2490171503/955514880

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

(23/24)^6

Exp ORIGINAL x power6 = 148035889/191102976

Exp term6 power over factorial := div(148035889/191102976, 720)

Exp term6 power over factorial = 148035889/137594142720

Exp cumulative sum through6 := sum(2490171503/955514880, 148035889/137594142720)

Exp cumulative sum through6 = 358732732321/137594142720

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

(23/24)^7

Exp ORIGINAL x power7 = 3404825447/4586471424

Exp term7 power over factorial := div(3404825447/4586471424, 5040)

Exp term7 power over factorial = 3404825447/23115815976960

Exp cumulative sum through7 := sum(358732732321/137594142720, 3404825447/23115815976960)

Exp cumulative sum through7 = 12054100771075/4623163195392

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

(23/24)^8

Exp ORIGINAL x power8 = 78310985281/110075314176

Exp term8 power over factorial := div(78310985281/110075314176, 40320)

Exp term8 power over factorial = 78310985281/4438236667576320

Exp cumulative sum through8 := sum(12054100771075/4623163195392, 78310985281/4438236667576320)

Exp cumulative sum through8 = 11572015051217281/4438236667576320

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

(23/24)^9

Exp ORIGINAL x power9 = 1801152661463/2641807540224

Exp term9 power over factorial := div(1801152661463/2641807540224, 362880)

Exp term9 power over factorial = 1801152661463/958659120196485120

Exp cumulative sum through9 := sum(11572015051217281/4438236667576320, 1801152661463/958659120196485120)

Exp cumulative sum through9 = 2499557052215594159/958659120196485120

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

(23/24)^10

Exp ORIGINAL x power10 = 41426511213649/63403380965376

Exp term10 power over factorial := div(41426511213649/63403380965376, 3628800)

Exp term10 power over factorial = 41426511213649/230078188847156428800

Exp cumulative sum through10 := sum(2499557052215594159/958659120196485120, 41426511213649/230078188847156428800)

Exp cumulative sum through10 = 599893733958253811809/230078188847156428800

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

(23/24)^11

Exp ORIGINAL x power11 = 952809757913927/1521681143169024

Exp term11 power over factorial := div(952809757913927/1521681143169024, 39916800)

Exp term11 power over factorial = 952809757913927/60740641855649297203200

Exp cumulative sum through11 := sum(599893733958253811809/230078188847156428800, 952809757913927/60740641855649297203200)

Exp cumulative sum through11 = 158371946717788764231503/60740641855649297203200

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

(23/24)^12

Exp ORIGINAL x power12 = 21914624432020321/36520347436056576

Exp term12 power over factorial := div(21914624432020321/36520347436056576, 479001600)

Exp term12 power over factorial = 21914624432020321/17493304854426997594521600

Exp cumulative sum through12 := sum(158371946717788764231503/60740641855649297203200, 21914624432020321/17493304854426997594521600)

Exp cumulative sum through12 = 9122224135327557706138637/3498660970885399518904320

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

(23/24)^13

Exp ORIGINAL x power13 = 504036361936467383/876488338465357824

Exp term13 power over factorial := div(504036361936467383/876488338465357824, 6227020800)

Exp term13 power over factorial = 504036361936467383/5457911114581223249490739200

Exp cumulative sum through13 := sum(9122224135327557706138637/3498660970885399518904320, 504036361936467383/5457911114581223249490739200)

Exp cumulative sum through13 = 14230669651615026383512741103/5457911114581223249490739200

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

(23/24)^14

Exp ORIGINAL x power14 = 11592836324538749809/21035720123168587776

Exp term14 power over factorial := div(11592836324538749809/21035720123168587776, 87178291200)

Exp term14 power over factorial = 11592836324538749809/1833858134499291011828888371200

Exp cumulative sum through14 := sum(14230669651615026383512741103/5457911114581223249490739200, 11592836324538749809/1833858134499291011828888371200)

Exp cumulative sum through14 = 4781505002954241701184819760417/1833858134499291011828888371200

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

(23/24)^15

Exp ORIGINAL x power15 = 266635235464391245607/504857282956046106624

Exp term15 power over factorial := div(266635235464391245607/504857282956046106624, 1307674368000)

Exp term15 power over factorial = 266635235464391245607/660188928419744764258399813632000

Exp cumulative sum through15 := sum(4781505002954241701184819760417/1833858134499291011828888371200, 266635235464391245607/660188928419744764258399813632000)

Exp cumulative sum through15 = 1721341801063793647661999504995727/660188928419744764258399813632000

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

(23/24)^16

Exp ORIGINAL x power16 = 6132610415680998648961/12116574790945106558976

Exp term16 power over factorial := div(6132610415680998648961/12116574790945106558976, 20922789888000)

Exp term16 power over factorial = 6132610415680998648961/253512548513181989475225528434688000

Exp cumulative sum through16 := sum(1721341801063793647661999504995727/660188928419744764258399813632000, 6132610415680998648961/253512548513181989475225528434688000)

Exp cumulative sum through16 = 660995251608502893312623490917008129/253512548513181989475225528434688000

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

(23/24)^17

Exp ORIGINAL x power17 = 141050039560662968926103/290797794982682557415424

Exp term17 power over factorial := div(141050039560662968926103/290797794982682557415424, 355687428096000)

Exp term17 power over factorial = 141050039560662968926103/103433119793378251705892015601352704000

Exp cumulative sum through17 := sum(660995251608502893312623490917008129/253512548513181989475225528434688000, 141050039560662968926103/103433119793378251705892015601352704000)

Exp cumulative sum through17 = 53937212531253864304317988991421648547/20686623958675650341178403120270540800

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

(23/24)^18

Exp ORIGINAL x power18 = 3244150909895248285300369/6979147079584381377970176

Exp term18 power over factorial := div(3244150909895248285300369/6979147079584381377970176, 6402373705728000)

Exp term18 power over factorial = 3244150909895248285300369/44683107750739404736945350739784368128000

Exp cumulative sum through18 := sum(53937212531253864304317988991421648547/20686623958675650341178403120270540800, 3244150909895248285300369/44683107750739404736945350739784368128000)

Exp cumulative sum through18 = 10591307187955304558316160556065367832899/4062100704612673157904122794525851648000

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

(23/24)^19

Exp ORIGINAL x power19 = 74615470927590710561908487/167499529910025153071284224

Exp term19 power over factorial := div(74615470927590710561908487/167499529910025153071284224, 121645100408832000)

Exp term19 power over factorial = 74615470927590710561908487/20375497134337168560047079937341671866368000

Exp cumulative sum through19 := sum(10591307187955304558316160556065367832899/4062100704612673157904122794525851648000, 74615470927590710561908487/20375497134337168560047079937341671866368000)

Exp cumulative sum through19 = 53125996854783807739129332276814595611729871/20375497134337168560047079937341671866368000

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

(23/24)^20

Exp ORIGINAL x power20 = 1716155831334586342923895201/4019988717840603673710821376

Exp term20 power over factorial := div(1716155831334586342923895201/4019988717840603673710821376, 2432902008176640000)

Exp term20 power over factorial = 1716155831334586342923895201/9780238624481840908822598369924002495856640000

Exp cumulative sum through20 := sum(53125996854783807739129332276814595611729871/20375497134337168560047079937341671866368000, 1716155831334586342923895201/9780238624481840908822598369924002495856640000)

Exp cumulative sum through20 = 1500028146488013395088131489659152484503190193/575308154381284759342505786466117793873920000

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

(23/24)^21

Exp ORIGINAL x power21 = 39471584120695485887249589623/96479729228174488169059713024

Exp term21 power over factorial := div(39471584120695485887249589623/96479729228174488169059713024, 51090942171709440000)

Exp term21 power over factorial = 39471584120695485887249589623/4929240266738847818046589578441697257911746560000

Exp cumulative sum through21 := sum(1500028146488013395088131489659152484503190193/575308154381284759342505786466117793873920000, 39471584120695485887249589623/4929240266738847818046589578441697257911746560000)

Exp cumulative sum through21 = 12852241159109298769154582187520313973110583163247/4929240266738847818046589578441697257911746560000

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

(23/24)^22

Exp ORIGINAL x power22 = 907846434775996175406740561329/2315513501476187716057433112576

Exp term22 power over factorial := div(907846434775996175406740561329/2315513501476187716057433112576, 1124000727777607680000)

Exp term22 power over factorial = 907846434775996175406740561329/2602638860838111647928599297417216152177402183680000

Exp cumulative sum through22 := sum(12852241159109298769154582187520313973110583163247/4929240266738847818046589578441697257911746560000, 907846434775996175406740561329/2602638860838111647928599297417216152177402183680000)

Exp cumulative sum through22 = 1357196666401941950022905448289100354795558930151149/520527772167622329585719859483443230435480436736000

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

(23/24)^23

Exp ORIGINAL x power23 = 20880467999847912034355032910567/55572324035428505185378394701824

Exp term23 power over factorial := div(20880467999847912034355032910567/55572324035428505185378394701824, 25852016738884976640000)

Exp term23 power over factorial = 907846434775996175406740561329/62463332660114679550286383138013187652257652408320000

Exp cumulative sum through23 := sum(1357196666401941950022905448289100354795558930151149/520527772167622329585719859483443230435480436736000, 907846434775996175406740561329/62463332660114679550286383138013187652257652408320000)

Exp cumulative sum through23 = 162863599968233034002749561641126818571642478358699209/62463332660114679550286383138013187652257652408320000

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

(23/24)^24

Exp ORIGINAL x power24 = 480250763996501976790165756943041/1333735776850284124449081472843776

Exp term24 power over factorial := div(480250763996501976790165756943041/1333735776850284124449081472843776, 620448401733239439360000)

Exp term24 power over factorial = 20880467999847912034355032910567/35978879612226055420964956687495596087700407787192320000

Exp cumulative sum through24 := sum(162863599968233034002749561641126818571642478358699209/62463332660114679550286383138013187652257652408320000, 20880467999847912034355032910567/35978879612226055420964956687495596087700407787192320000)

Exp cumulative sum through24 = 93809433581702227585583768385757047345178101889643654951/35978879612226055420964956687495596087700407787192320000

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

(23/24)^25

Exp ORIGINAL x power25 = 11045767571919545466173812409689943/32009658644406818986777955348250624

Exp term25 power over factorial := div(11045767571919545466173812409689943/32009658644406818986777955348250624, 15511210043330985984000000)

Exp term25 power over factorial = 480250763996501976790165756943041/21587327767335633252578974012497357652620244672315392000000

Exp cumulative sum through25 := sum(93809433581702227585583768385757047345178101889643654951/35978879612226055420964956687495596087700407787192320000, 480250763996501976790165756943041/21587327767335633252578974012497357652620244672315392000000)

Exp cumulative sum through25 = 56285660149021336551350261511704992403608837923951949913641/21587327767335633252578974012497357652620244672315392000000

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

(23/24)^26

Exp ORIGINAL x power26 = 254052654154149545721997685422868689/768231807465763655682670928358014976

Exp term26 power over factorial := div(254052654154149545721997685422868689/768231807465763655682670928358014976, 403291461126605635584000000)

Exp term26 power over factorial = 11045767571919545466173812409689943/13470492526817435149609279783798351175235032675524804608000000

Exp cumulative sum through26 := sum(56285660149021336551350261511704992403608837923951949913641/21587327767335633252578974012497357652620244672315392000000, 11045767571919545466173812409689943/13470492526817435149609279783798351175235032675524804608000000)

Exp cumulative sum through26 = 35122251932989314008042563194349682831771460330719829155801927/13470492526817435149609279783798351175235032675524804608000000

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

(23/24)^27

Exp ORIGINAL x power27 = 5843211045545439551605946764725979847/18437563379178327736384102280592359424

Exp term27 power over factorial := div(5843211045545439551605946764725979847/18437563379178327736384102280592359424, 10888869450418352160768000000)

Exp term27 power over factorial = 254052654154149545721997685422868689/8728879157377697976946813299901331561552301173740073385984000000

Exp cumulative sum through27 := sum(35122251932989314008042563194349682831771460330719829155801927/13470492526817435149609279783798351175235032675524804608000000, 254052654154149545721997685422868689/8728879157377697976946813299901331561552301173740073385984000000)

Exp cumulative sum through27 = 4551843850515415095442316190038529425828411168005689395676503477/1745775831475539595389362659980266312310460234748014677196800000

source roles = [23/24, 27, [1, 23/24, 529/1152, 12167/82944, 279841/7962624, 6436343/955514880, 148035889/137594142720, 3404825447/23115815976960, 78310985281/4438236667576320, 1801152661463/958659120196485120, 41426511213649/230078188847156428800, 952809757913927/60740641855649297203200, 21914624432020321/17493304854426997594521600, 504036361936467383/5457911114581223249490739200, 11592836324538749809/1833858134499291011828888371200, 266635235464391245607/660188928419744764258399813632000, 6132610415680998648961/253512548513181989475225528434688000, 141050039560662968926103/103433119793378251705892015601352704000, 3244150909895248285300369/44683107750739404736945350739784368128000, 74615470927590710561908487/20375497134337168560047079937341671866368000, 1716155831334586342923895201/9780238624481840908822598369924002495856640000, 39471584120695485887249589623/4929240266738847818046589578441697257911746560000, 907846434775996175406740561329/2602638860838111647928599297417216152177402183680000, 907846434775996175406740561329/62463332660114679550286383138013187652257652408320000, 20880467999847912034355032910567/35978879612226055420964956687495596087700407787192320000, 480250763996501976790165756943041/21587327767335633252578974012497357652620244672315392000000, 11045767571919545466173812409689943/13470492526817435149609279783798351175235032675524804608000000, 254052654154149545721997685422868689/8728879157377697976946813299901331561552301173740073385984000000], [1, 47/24, 2785/1152, 212687/82944, 20697793/7962624, 2490171503/955514880, 358732732321/137594142720, 12054100771075/4623163195392, 11572015051217281/4438236667576320, 2499557052215594159/958659120196485120, 599893733958253811809/230078188847156428800, 158371946717788764231503/60740641855649297203200, 9122224135327557706138637/3498660970885399518904320, 14230669651615026383512741103/5457911114581223249490739200, 4781505002954241701184819760417/1833858134499291011828888371200, 1721341801063793647661999504995727/660188928419744764258399813632000, 660995251608502893312623490917008129/253512548513181989475225528434688000, 53937212531253864304317988991421648547/20686623958675650341178403120270540800, 10591307187955304558316160556065367832899/4062100704612673157904122794525851648000, 53125996854783807739129332276814595611729871/20375497134337168560047079937341671866368000, 1500028146488013395088131489659152484503190193/575308154381284759342505786466117793873920000, 12852241159109298769154582187520313973110583163247/4929240266738847818046589578441697257911746560000, 1357196666401941950022905448289100354795558930151149/520527772167622329585719859483443230435480436736000, 162863599968233034002749561641126818571642478358699209/62463332660114679550286383138013187652257652408320000, 93809433581702227585583768385757047345178101889643654951/35978879612226055420964956687495596087700407787192320000, 56285660149021336551350261511704992403608837923951949913641/21587327767335633252578974012497357652620244672315392000000, 35122251932989314008042563194349682831771460330719829155801927/13470492526817435149609279783798351175235032675524804608000000, 4551843850515415095442316190038529425828411168005689395676503477/1745775831475539595389362659980266312310460234748014677196800000]]

derived = [4551843850515415095442316190038529425828411168005689395676503477/1745775831475539595389362659980266312310460234748014677196800000, No, finite sum is not a general infinite-value certificate]

Reverse checks

• S465 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• 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

(23/24, 27, [1, 23/24, 529/1152, 12167/82944, 279841/7962624, 6436343/955514880, 148035889/137594142720, 3404825447/23115815976960, 78310985281/4438236667576320, 1801152661463/958659120196485120, 41426511213649/230078188847156428800, 952809757913927/60740641855649297203200, 21914624432020321/17493304854426997594521600, 504036361936467383/5457911114581223249490739200, 11592836324538749809/1833858134499291011828888371200, 266635235464391245607/660188928419744764258399813632000, 6132610415680998648961/253512548513181989475225528434688000, 141050039560662968926103/103433119793378251705892015601352704000, 3244150909895248285300369/44683107750739404736945350739784368128000, 74615470927590710561908487/20375497134337168560047079937341671866368000, 1716155831334586342923895201/9780238624481840908822598369924002495856640000, 39471584120695485887249589623/4929240266738847818046589578441697257911746560000, 907846434775996175406740561329/2602638860838111647928599297417216152177402183680000, 907846434775996175406740561329/62463332660114679550286383138013187652257652408320000, 20880467999847912034355032910567/35978879612226055420964956687495596087700407787192320000, 480250763996501976790165756943041/21587327767335633252578974012497357652620244672315392000000, 11045767571919545466173812409689943/13470492526817435149609279783798351175235032675524804608000000, 254052654154149545721997685422868689/8728879157377697976946813299901331561552301173740073385984000000], [1, 47/24, 2785/1152, 212687/82944, 20697793/7962624, 2490171503/955514880, 358732732321/137594142720, 12054100771075/4623163195392, 11572015051217281/4438236667576320, 2499557052215594159/958659120196485120, 599893733958253811809/230078188847156428800, 158371946717788764231503/60740641855649297203200, 9122224135327557706138637/3498660970885399518904320, 14230669651615026383512741103/5457911114581223249490739200, 4781505002954241701184819760417/1833858134499291011828888371200, 1721341801063793647661999504995727/660188928419744764258399813632000, 660995251608502893312623490917008129/253512548513181989475225528434688000, 53937212531253864304317988991421648547/20686623958675650341178403120270540800, 10591307187955304558316160556065367832899/4062100704612673157904122794525851648000, 53125996854783807739129332276814595611729871/20375497134337168560047079937341671866368000, 1500028146488013395088131489659152484503190193/575308154381284759342505786466117793873920000, 12852241159109298769154582187520313973110583163247/4929240266738847818046589578441697257911746560000, 1357196666401941950022905448289100354795558930151149/520527772167622329585719859483443230435480436736000, 162863599968233034002749561641126818571642478358699209/62463332660114679550286383138013187652257652408320000, 93809433581702227585583768385757047345178101889643654951/35978879612226055420964956687495596087700407787192320000, 56285660149021336551350261511704992403608837923951949913641/21587327767335633252578974012497357652620244672315392000000, 35122251932989314008042563194349682831771460330719829155801927/13470492526817435149609279783798351175235032675524804608000000, 4551843850515415095442316190038529425828411168005689395676503477/1745775831475539595389362659980266312310460234748014677196800000], 4551843850515415095442316190038529425828411168005689395676503477/1745775831475539595389362659980266312310460234748014677196800000, 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.