第 17587 題：函數列逐點收斂

原題與已知條件

同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[11,12],"coefficients":[12,-13],"shift":2,"prefix_length":12}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。

• G001 — 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[11,12],"coefficients":[12,-13],"shift":2,"prefix_length":12}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-pointwise-convergence-of-functions

逐步推導

same COMPLETE finite domain Fin(2);original aligned limits=[11, 12];signed coefficients=[12, -13];positive shift=2

declared for EVERY n>=0:f_n(x)=limit[x]+coefficient[x]/(n+shift);signed error=f_n(x)-limit[x]=coefficient[x]/(n+shift)

finite prefix point0 index0 denominator := sum(0, 2)

finite prefix point0 index0 denominator = 2

finite prefix point0 index0 signed correction := div(12, 2)

finite prefix point0 index0 signed correction = 6

finite prefix point0 index0 function value := sum(11, 6)

finite prefix point0 index0 function value = 17

finite prefix point0 index0 reverse signed error := sub(17, 11)

finite prefix point0 index0 reverse signed error = 6

finite prefix point0 index0:original point=0;n=0;limit=11;signed coefficient=12

f_n(x)=17;f_n(x)-limit=6;this error field remains SIGNED

finite prefix point0 index1 denominator := sum(1, 2)

finite prefix point0 index1 denominator = 3

finite prefix point0 index1 signed correction := div(12, 3)

finite prefix point0 index1 signed correction = 4

finite prefix point0 index1 function value := sum(11, 4)

finite prefix point0 index1 function value = 15

finite prefix point0 index1 reverse signed error := sub(15, 11)

finite prefix point0 index1 reverse signed error = 4

finite prefix point0 index1:original point=0;n=1;limit=11;signed coefficient=12

f_n(x)=15;f_n(x)-limit=4;this error field remains SIGNED

finite prefix point0 index2 denominator := sum(2, 2)

finite prefix point0 index2 denominator = 4

finite prefix point0 index2 signed correction := div(12, 4)

finite prefix point0 index2 signed correction = 3

finite prefix point0 index2 function value := sum(11, 3)

finite prefix point0 index2 function value = 14

finite prefix point0 index2 reverse signed error := sub(14, 11)

finite prefix point0 index2 reverse signed error = 3

finite prefix point0 index2:original point=0;n=2;limit=11;signed coefficient=12

f_n(x)=14;f_n(x)-limit=3;this error field remains SIGNED

finite prefix point0 index3 denominator := sum(3, 2)

finite prefix point0 index3 denominator = 5

finite prefix point0 index3 signed correction := div(12, 5)

finite prefix point0 index3 signed correction = 12/5

finite prefix point0 index3 function value := sum(11, 12/5)

finite prefix point0 index3 function value = 67/5

finite prefix point0 index3 reverse signed error := sub(67/5, 11)

finite prefix point0 index3 reverse signed error = 12/5

finite prefix point0 index3:original point=0;n=3;limit=11;signed coefficient=12

f_n(x)=67/5;f_n(x)-limit=12/5;this error field remains SIGNED

finite prefix point0 index4 denominator := sum(4, 2)

finite prefix point0 index4 denominator = 6

finite prefix point0 index4 signed correction := div(12, 6)

finite prefix point0 index4 signed correction = 2

finite prefix point0 index4 function value := sum(11, 2)

finite prefix point0 index4 function value = 13

finite prefix point0 index4 reverse signed error := sub(13, 11)

finite prefix point0 index4 reverse signed error = 2

finite prefix point0 index4:original point=0;n=4;limit=11;signed coefficient=12

f_n(x)=13;f_n(x)-limit=2;this error field remains SIGNED

finite prefix point0 index5 denominator := sum(5, 2)

finite prefix point0 index5 denominator = 7

finite prefix point0 index5 signed correction := div(12, 7)

finite prefix point0 index5 signed correction = 12/7

finite prefix point0 index5 function value := sum(11, 12/7)

finite prefix point0 index5 function value = 89/7

finite prefix point0 index5 reverse signed error := sub(89/7, 11)

finite prefix point0 index5 reverse signed error = 12/7

finite prefix point0 index5:original point=0;n=5;limit=11;signed coefficient=12

f_n(x)=89/7;f_n(x)-limit=12/7;this error field remains SIGNED

finite prefix point0 index6 denominator := sum(6, 2)

finite prefix point0 index6 denominator = 8

finite prefix point0 index6 signed correction := div(12, 8)

finite prefix point0 index6 signed correction = 3/2

finite prefix point0 index6 function value := sum(11, 3/2)

finite prefix point0 index6 function value = 25/2

finite prefix point0 index6 reverse signed error := sub(25/2, 11)

finite prefix point0 index6 reverse signed error = 3/2

finite prefix point0 index6:original point=0;n=6;limit=11;signed coefficient=12

f_n(x)=25/2;f_n(x)-limit=3/2;this error field remains SIGNED

finite prefix point0 index7 denominator := sum(7, 2)

finite prefix point0 index7 denominator = 9

finite prefix point0 index7 signed correction := div(12, 9)

finite prefix point0 index7 signed correction = 4/3

finite prefix point0 index7 function value := sum(11, 4/3)

finite prefix point0 index7 function value = 37/3

finite prefix point0 index7 reverse signed error := sub(37/3, 11)

finite prefix point0 index7 reverse signed error = 4/3

finite prefix point0 index7:original point=0;n=7;limit=11;signed coefficient=12

f_n(x)=37/3;f_n(x)-limit=4/3;this error field remains SIGNED

finite prefix point0 index8 denominator := sum(8, 2)

finite prefix point0 index8 denominator = 10

finite prefix point0 index8 signed correction := div(12, 10)

finite prefix point0 index8 signed correction = 6/5

finite prefix point0 index8 function value := sum(11, 6/5)

finite prefix point0 index8 function value = 61/5

finite prefix point0 index8 reverse signed error := sub(61/5, 11)

finite prefix point0 index8 reverse signed error = 6/5

finite prefix point0 index8:original point=0;n=8;limit=11;signed coefficient=12

f_n(x)=61/5;f_n(x)-limit=6/5;this error field remains SIGNED

finite prefix point0 index9 denominator := sum(9, 2)

finite prefix point0 index9 denominator = 11

finite prefix point0 index9 signed correction := div(12, 11)

finite prefix point0 index9 signed correction = 12/11

finite prefix point0 index9 function value := sum(11, 12/11)

finite prefix point0 index9 function value = 133/11

finite prefix point0 index9 reverse signed error := sub(133/11, 11)

finite prefix point0 index9 reverse signed error = 12/11

finite prefix point0 index9:original point=0;n=9;limit=11;signed coefficient=12

f_n(x)=133/11;f_n(x)-limit=12/11;this error field remains SIGNED

finite prefix point0 index10 denominator := sum(10, 2)

finite prefix point0 index10 denominator = 12

finite prefix point0 index10 signed correction := div(12, 12)

finite prefix point0 index10 signed correction = 1

finite prefix point0 index10 function value := sum(11, 1)

finite prefix point0 index10 function value = 12

finite prefix point0 index10 reverse signed error := sub(12, 11)

finite prefix point0 index10 reverse signed error = 1

finite prefix point0 index10:original point=0;n=10;limit=11;signed coefficient=12

f_n(x)=12;f_n(x)-limit=1;this error field remains SIGNED

finite prefix point0 index11 denominator := sum(11, 2)

finite prefix point0 index11 denominator = 13

finite prefix point0 index11 signed correction := div(12, 13)

finite prefix point0 index11 signed correction = 12/13

finite prefix point0 index11 function value := sum(11, 12/13)

finite prefix point0 index11 function value = 155/13

finite prefix point0 index11 reverse signed error := sub(155/13, 11)

finite prefix point0 index11 reverse signed error = 12/13

finite prefix point0 index11:original point=0;n=11;limit=11;signed coefficient=12

f_n(x)=155/13;f_n(x)-limit=12/13;this error field remains SIGNED

finite prefix point1 index0 denominator := sum(0, 2)

finite prefix point1 index0 denominator = 2

finite prefix point1 index0 signed correction := div(-13, 2)

finite prefix point1 index0 signed correction = -13/2

finite prefix point1 index0 function value := sum(12, -13/2)

finite prefix point1 index0 function value = 11/2

finite prefix point1 index0 reverse signed error := sub(11/2, 12)

finite prefix point1 index0 reverse signed error = -13/2

finite prefix point1 index0:original point=1;n=0;limit=12;signed coefficient=-13

f_n(x)=11/2;f_n(x)-limit=-13/2;this error field remains SIGNED

finite prefix point1 index1 denominator := sum(1, 2)

finite prefix point1 index1 denominator = 3

finite prefix point1 index1 signed correction := div(-13, 3)

finite prefix point1 index1 signed correction = -13/3

finite prefix point1 index1 function value := sum(12, -13/3)

finite prefix point1 index1 function value = 23/3

finite prefix point1 index1 reverse signed error := sub(23/3, 12)

finite prefix point1 index1 reverse signed error = -13/3

finite prefix point1 index1:original point=1;n=1;limit=12;signed coefficient=-13

f_n(x)=23/3;f_n(x)-limit=-13/3;this error field remains SIGNED

finite prefix point1 index2 denominator := sum(2, 2)

finite prefix point1 index2 denominator = 4

finite prefix point1 index2 signed correction := div(-13, 4)

finite prefix point1 index2 signed correction = -13/4

finite prefix point1 index2 function value := sum(12, -13/4)

finite prefix point1 index2 function value = 35/4

finite prefix point1 index2 reverse signed error := sub(35/4, 12)

finite prefix point1 index2 reverse signed error = -13/4

finite prefix point1 index2:original point=1;n=2;limit=12;signed coefficient=-13

f_n(x)=35/4;f_n(x)-limit=-13/4;this error field remains SIGNED

finite prefix point1 index3 denominator := sum(3, 2)

finite prefix point1 index3 denominator = 5

finite prefix point1 index3 signed correction := div(-13, 5)

finite prefix point1 index3 signed correction = -13/5

finite prefix point1 index3 function value := sum(12, -13/5)

finite prefix point1 index3 function value = 47/5

finite prefix point1 index3 reverse signed error := sub(47/5, 12)

finite prefix point1 index3 reverse signed error = -13/5

finite prefix point1 index3:original point=1;n=3;limit=12;signed coefficient=-13

f_n(x)=47/5;f_n(x)-limit=-13/5;this error field remains SIGNED

finite prefix point1 index4 denominator := sum(4, 2)

finite prefix point1 index4 denominator = 6

finite prefix point1 index4 signed correction := div(-13, 6)

finite prefix point1 index4 signed correction = -13/6

finite prefix point1 index4 function value := sum(12, -13/6)

finite prefix point1 index4 function value = 59/6

finite prefix point1 index4 reverse signed error := sub(59/6, 12)

finite prefix point1 index4 reverse signed error = -13/6

finite prefix point1 index4:original point=1;n=4;limit=12;signed coefficient=-13

f_n(x)=59/6;f_n(x)-limit=-13/6;this error field remains SIGNED

finite prefix point1 index5 denominator := sum(5, 2)

finite prefix point1 index5 denominator = 7

finite prefix point1 index5 signed correction := div(-13, 7)

finite prefix point1 index5 signed correction = -13/7

finite prefix point1 index5 function value := sum(12, -13/7)

finite prefix point1 index5 function value = 71/7

finite prefix point1 index5 reverse signed error := sub(71/7, 12)

finite prefix point1 index5 reverse signed error = -13/7

finite prefix point1 index5:original point=1;n=5;limit=12;signed coefficient=-13

f_n(x)=71/7;f_n(x)-limit=-13/7;this error field remains SIGNED

finite prefix point1 index6 denominator := sum(6, 2)

finite prefix point1 index6 denominator = 8

finite prefix point1 index6 signed correction := div(-13, 8)

finite prefix point1 index6 signed correction = -13/8

finite prefix point1 index6 function value := sum(12, -13/8)

finite prefix point1 index6 function value = 83/8

finite prefix point1 index6 reverse signed error := sub(83/8, 12)

finite prefix point1 index6 reverse signed error = -13/8

finite prefix point1 index6:original point=1;n=6;limit=12;signed coefficient=-13

f_n(x)=83/8;f_n(x)-limit=-13/8;this error field remains SIGNED

finite prefix point1 index7 denominator := sum(7, 2)

finite prefix point1 index7 denominator = 9

finite prefix point1 index7 signed correction := div(-13, 9)

finite prefix point1 index7 signed correction = -13/9

finite prefix point1 index7 function value := sum(12, -13/9)

finite prefix point1 index7 function value = 95/9

finite prefix point1 index7 reverse signed error := sub(95/9, 12)

finite prefix point1 index7 reverse signed error = -13/9

finite prefix point1 index7:original point=1;n=7;limit=12;signed coefficient=-13

f_n(x)=95/9;f_n(x)-limit=-13/9;this error field remains SIGNED

finite prefix point1 index8 denominator := sum(8, 2)

finite prefix point1 index8 denominator = 10

finite prefix point1 index8 signed correction := div(-13, 10)

finite prefix point1 index8 signed correction = -13/10

finite prefix point1 index8 function value := sum(12, -13/10)

finite prefix point1 index8 function value = 107/10

finite prefix point1 index8 reverse signed error := sub(107/10, 12)

finite prefix point1 index8 reverse signed error = -13/10

finite prefix point1 index8:original point=1;n=8;limit=12;signed coefficient=-13

f_n(x)=107/10;f_n(x)-limit=-13/10;this error field remains SIGNED

finite prefix point1 index9 denominator := sum(9, 2)

finite prefix point1 index9 denominator = 11

finite prefix point1 index9 signed correction := div(-13, 11)

finite prefix point1 index9 signed correction = -13/11

finite prefix point1 index9 function value := sum(12, -13/11)

finite prefix point1 index9 function value = 119/11

finite prefix point1 index9 reverse signed error := sub(119/11, 12)

finite prefix point1 index9 reverse signed error = -13/11

finite prefix point1 index9:original point=1;n=9;limit=12;signed coefficient=-13

f_n(x)=119/11;f_n(x)-limit=-13/11;this error field remains SIGNED

finite prefix point1 index10 denominator := sum(10, 2)

finite prefix point1 index10 denominator = 12

finite prefix point1 index10 signed correction := div(-13, 12)

finite prefix point1 index10 signed correction = -13/12

finite prefix point1 index10 function value := sum(12, -13/12)

finite prefix point1 index10 function value = 131/12

finite prefix point1 index10 reverse signed error := sub(131/12, 12)

finite prefix point1 index10 reverse signed error = -13/12

finite prefix point1 index10:original point=1;n=10;limit=12;signed coefficient=-13

f_n(x)=131/12;f_n(x)-limit=-13/12;this error field remains SIGNED

finite prefix point1 index11 denominator := sum(11, 2)

finite prefix point1 index11 denominator = 13

finite prefix point1 index11 signed correction := div(-13, 13)

finite prefix point1 index11 signed correction = -1

finite prefix point1 index11 function value := sum(12, -1)

finite prefix point1 index11 function value = 11

finite prefix point1 index11 reverse signed error := sub(11, 12)

finite prefix point1 index11 reverse signed error = -1

finite prefix point1 index11:original point=1;n=11;limit=12;signed coefficient=-13

f_n(x)=11;f_n(x)-limit=-1;this error field remains SIGNED

finite observed length=12;complete domain-order rows=[[0, [17, 15, 14, 67/5, 13, 89/7, 25/2, 37/3, 61/5, 133/11, 12, 155/13]], [1, [11/2, 23/3, 35/4, 47/5, 59/6, 71/7, 83/8, 95/9, 107/10, 119/11, 131/12, 11]]]

prefix-alone sufficiency=否;finite_prefix_not_pointwise_convergence_certificate

逐步反向核對

• S122 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S121 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S120 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index11 reverse signed error，不以小數近似替代。
• S119 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index11 function value，不以小數近似替代。
• S118 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index11 signed correction，不以小數近似替代。
• S117 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index11 denominator，不以小數近似替代。
• S116 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S115 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index10 reverse signed error，不以小數近似替代。
• S114 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index10 function value，不以小數近似替代。
• S113 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index10 signed correction，不以小數近似替代。
• S112 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index10 denominator，不以小數近似替代。
• S111 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S110 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index9 reverse signed error，不以小數近似替代。
• S109 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index9 function value，不以小數近似替代。
• S108 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index9 signed correction，不以小數近似替代。
• S107 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index9 denominator，不以小數近似替代。
• S106 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S105 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index8 reverse signed error，不以小數近似替代。
• S104 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index8 function value，不以小數近似替代。
• S103 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index8 signed correction，不以小數近似替代。
• S102 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index8 denominator，不以小數近似替代。
• S101 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S100 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index7 reverse signed error，不以小數近似替代。
• S099 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index7 function value，不以小數近似替代。
• S098 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index7 signed correction，不以小數近似替代。
• S097 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index7 denominator，不以小數近似替代。
• S096 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S095 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index6 reverse signed error，不以小數近似替代。
• S094 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index6 function value，不以小數近似替代。
• S093 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index6 signed correction，不以小數近似替代。
• S092 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index6 denominator，不以小數近似替代。
• S091 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S090 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index5 reverse signed error，不以小數近似替代。
• S089 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index5 function value，不以小數近似替代。
• S088 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index5 signed correction，不以小數近似替代。
• S087 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index5 denominator，不以小數近似替代。
• S086 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S085 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index4 reverse signed error，不以小數近似替代。
• S084 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index4 function value，不以小數近似替代。
• S083 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index4 signed correction，不以小數近似替代。
• S082 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index4 denominator，不以小數近似替代。
• S081 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S080 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index3 reverse signed error，不以小數近似替代。
• S079 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index3 function value，不以小數近似替代。
• S078 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index3 signed correction，不以小數近似替代。
• S077 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index3 denominator，不以小數近似替代。
• S076 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S075 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index2 reverse signed error，不以小數近似替代。
• S074 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index2 function value，不以小數近似替代。
• S073 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index2 signed correction，不以小數近似替代。
• S072 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index2 denominator，不以小數近似替代。
• S071 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S070 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index1 reverse signed error，不以小數近似替代。
• S069 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index1 function value，不以小數近似替代。
• S068 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index1 signed correction，不以小數近似替代。
• S067 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index1 denominator，不以小數近似替代。
• S066 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S065 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index0 reverse signed error，不以小數近似替代。
• S064 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index0 function value，不以小數近似替代。
• S063 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index0 signed correction，不以小數近似替代。
• S062 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index0 denominator，不以小數近似替代。
• S061 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S060 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index11 reverse signed error，不以小數近似替代。
• S059 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index11 function value，不以小數近似替代。
• S058 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index11 signed correction，不以小數近似替代。
• S057 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index11 denominator，不以小數近似替代。
• S056 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S055 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index10 reverse signed error，不以小數近似替代。
• S054 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index10 function value，不以小數近似替代。
• S053 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index10 signed correction，不以小數近似替代。
• S052 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index10 denominator，不以小數近似替代。
• S051 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S050 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index9 reverse signed error，不以小數近似替代。
• S049 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index9 function value，不以小數近似替代。
• S048 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index9 signed correction，不以小數近似替代。
• S047 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index9 denominator，不以小數近似替代。
• S046 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S045 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index8 reverse signed error，不以小數近似替代。
• S044 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index8 function value，不以小數近似替代。
• S043 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index8 signed correction，不以小數近似替代。
• S042 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index8 denominator，不以小數近似替代。
• S041 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S040 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index7 reverse signed error，不以小數近似替代。
• S039 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index7 function value，不以小數近似替代。
• S038 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index7 signed correction，不以小數近似替代。
• S037 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index7 denominator，不以小數近似替代。
• S036 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S035 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index6 reverse signed error，不以小數近似替代。
• S034 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index6 function value，不以小數近似替代。
• S033 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index6 signed correction，不以小數近似替代。
• S032 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index6 denominator，不以小數近似替代。
• S031 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S030 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index5 reverse signed error，不以小數近似替代。
• S029 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index5 function value，不以小數近似替代。
• S028 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index5 signed correction，不以小數近似替代。
• S027 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index5 denominator，不以小數近似替代。
• S026 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S025 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index4 reverse signed error，不以小數近似替代。
• S024 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index4 function value，不以小數近似替代。
• S023 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index4 signed correction，不以小數近似替代。
• S022 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index4 denominator，不以小數近似替代。
• S021 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S020 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index3 reverse signed error，不以小數近似替代。
• S019 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index3 function value，不以小數近似替代。
• S018 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index3 signed correction，不以小數近似替代。
• S017 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index3 denominator，不以小數近似替代。
• S016 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S015 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index2 reverse signed error，不以小數近似替代。
• S014 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index2 function value，不以小數近似替代。
• S013 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index2 signed correction，不以小數近似替代。
• S012 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index2 denominator，不以小數近似替代。
• S011 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S010 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index1 reverse signed error，不以小數近似替代。
• S009 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index1 function value，不以小數近似替代。
• S008 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index1 signed correction，不以小數近似替代。
• S007 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index1 denominator，不以小數近似替代。
• S006 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S005 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index0 reverse signed error，不以小數近似替代。
• S004 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index0 function value，不以小數近似替代。
• S003 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index0 signed correction，不以小數近似替代。
• S002 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index0 denominator，不以小數近似替代。
• S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。

結論

(12, [[0, [17, 15, 14, 67/5, 13, 89/7, 25/2, 37/3, 61/5, 133/11, 12, 155/13]], [1, [11/2, 23/3, 35/4, 47/5, 59/6, 71/7, 83/8, 95/9, 107/10, 119/11, 131/12, 11]]], 否, finite_prefix_not_pointwise_convergence_certificate)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。