第 17589 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":[13,14],"coefficients":[14,-15],"shift":2,"prefix_length":14}。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":[13,14],"coefficients":[14,-15],"shift":2,"prefix_length":14}。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=[13, 14];signed coefficients=[14, -15];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(14, 2)

finite prefix point0 index0 signed correction = 7

finite prefix point0 index0 function value := sum(13, 7)

finite prefix point0 index0 function value = 20

finite prefix point0 index0 reverse signed error := sub(20, 13)

finite prefix point0 index0 reverse signed error = 7

finite prefix point0 index0:original point=0;n=0;limit=13;signed coefficient=14

f_n(x)=20;f_n(x)-limit=7;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(14, 3)

finite prefix point0 index1 signed correction = 14/3

finite prefix point0 index1 function value := sum(13, 14/3)

finite prefix point0 index1 function value = 53/3

finite prefix point0 index1 reverse signed error := sub(53/3, 13)

finite prefix point0 index1 reverse signed error = 14/3

finite prefix point0 index1:original point=0;n=1;limit=13;signed coefficient=14

f_n(x)=53/3;f_n(x)-limit=14/3;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(14, 4)

finite prefix point0 index2 signed correction = 7/2

finite prefix point0 index2 function value := sum(13, 7/2)

finite prefix point0 index2 function value = 33/2

finite prefix point0 index2 reverse signed error := sub(33/2, 13)

finite prefix point0 index2 reverse signed error = 7/2

finite prefix point0 index2:original point=0;n=2;limit=13;signed coefficient=14

f_n(x)=33/2;f_n(x)-limit=7/2;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(14, 5)

finite prefix point0 index3 signed correction = 14/5

finite prefix point0 index3 function value := sum(13, 14/5)

finite prefix point0 index3 function value = 79/5

finite prefix point0 index3 reverse signed error := sub(79/5, 13)

finite prefix point0 index3 reverse signed error = 14/5

finite prefix point0 index3:original point=0;n=3;limit=13;signed coefficient=14

f_n(x)=79/5;f_n(x)-limit=14/5;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(14, 6)

finite prefix point0 index4 signed correction = 7/3

finite prefix point0 index4 function value := sum(13, 7/3)

finite prefix point0 index4 function value = 46/3

finite prefix point0 index4 reverse signed error := sub(46/3, 13)

finite prefix point0 index4 reverse signed error = 7/3

finite prefix point0 index4:original point=0;n=4;limit=13;signed coefficient=14

f_n(x)=46/3;f_n(x)-limit=7/3;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(14, 7)

finite prefix point0 index5 signed correction = 2

finite prefix point0 index5 function value := sum(13, 2)

finite prefix point0 index5 function value = 15

finite prefix point0 index5 reverse signed error := sub(15, 13)

finite prefix point0 index5 reverse signed error = 2

finite prefix point0 index5:original point=0;n=5;limit=13;signed coefficient=14

f_n(x)=15;f_n(x)-limit=2;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(14, 8)

finite prefix point0 index6 signed correction = 7/4

finite prefix point0 index6 function value := sum(13, 7/4)

finite prefix point0 index6 function value = 59/4

finite prefix point0 index6 reverse signed error := sub(59/4, 13)

finite prefix point0 index6 reverse signed error = 7/4

finite prefix point0 index6:original point=0;n=6;limit=13;signed coefficient=14

f_n(x)=59/4;f_n(x)-limit=7/4;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(14, 9)

finite prefix point0 index7 signed correction = 14/9

finite prefix point0 index7 function value := sum(13, 14/9)

finite prefix point0 index7 function value = 131/9

finite prefix point0 index7 reverse signed error := sub(131/9, 13)

finite prefix point0 index7 reverse signed error = 14/9

finite prefix point0 index7:original point=0;n=7;limit=13;signed coefficient=14

f_n(x)=131/9;f_n(x)-limit=14/9;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(14, 10)

finite prefix point0 index8 signed correction = 7/5

finite prefix point0 index8 function value := sum(13, 7/5)

finite prefix point0 index8 function value = 72/5

finite prefix point0 index8 reverse signed error := sub(72/5, 13)

finite prefix point0 index8 reverse signed error = 7/5

finite prefix point0 index8:original point=0;n=8;limit=13;signed coefficient=14

f_n(x)=72/5;f_n(x)-limit=7/5;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(14, 11)

finite prefix point0 index9 signed correction = 14/11

finite prefix point0 index9 function value := sum(13, 14/11)

finite prefix point0 index9 function value = 157/11

finite prefix point0 index9 reverse signed error := sub(157/11, 13)

finite prefix point0 index9 reverse signed error = 14/11

finite prefix point0 index9:original point=0;n=9;limit=13;signed coefficient=14

f_n(x)=157/11;f_n(x)-limit=14/11;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(14, 12)

finite prefix point0 index10 signed correction = 7/6

finite prefix point0 index10 function value := sum(13, 7/6)

finite prefix point0 index10 function value = 85/6

finite prefix point0 index10 reverse signed error := sub(85/6, 13)

finite prefix point0 index10 reverse signed error = 7/6

finite prefix point0 index10:original point=0;n=10;limit=13;signed coefficient=14

f_n(x)=85/6;f_n(x)-limit=7/6;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(14, 13)

finite prefix point0 index11 signed correction = 14/13

finite prefix point0 index11 function value := sum(13, 14/13)

finite prefix point0 index11 function value = 183/13

finite prefix point0 index11 reverse signed error := sub(183/13, 13)

finite prefix point0 index11 reverse signed error = 14/13

finite prefix point0 index11:original point=0;n=11;limit=13;signed coefficient=14

f_n(x)=183/13;f_n(x)-limit=14/13;this error field remains SIGNED

finite prefix point0 index12 denominator := sum(12, 2)

finite prefix point0 index12 denominator = 14

finite prefix point0 index12 signed correction := div(14, 14)

finite prefix point0 index12 signed correction = 1

finite prefix point0 index12 function value := sum(13, 1)

finite prefix point0 index12 function value = 14

finite prefix point0 index12 reverse signed error := sub(14, 13)

finite prefix point0 index12 reverse signed error = 1

finite prefix point0 index12:original point=0;n=12;limit=13;signed coefficient=14

f_n(x)=14;f_n(x)-limit=1;this error field remains SIGNED

finite prefix point0 index13 denominator := sum(13, 2)

finite prefix point0 index13 denominator = 15

finite prefix point0 index13 signed correction := div(14, 15)

finite prefix point0 index13 signed correction = 14/15

finite prefix point0 index13 function value := sum(13, 14/15)

finite prefix point0 index13 function value = 209/15

finite prefix point0 index13 reverse signed error := sub(209/15, 13)

finite prefix point0 index13 reverse signed error = 14/15

finite prefix point0 index13:original point=0;n=13;limit=13;signed coefficient=14

f_n(x)=209/15;f_n(x)-limit=14/15;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(-15, 2)

finite prefix point1 index0 signed correction = -15/2

finite prefix point1 index0 function value := sum(14, -15/2)

finite prefix point1 index0 function value = 13/2

finite prefix point1 index0 reverse signed error := sub(13/2, 14)

finite prefix point1 index0 reverse signed error = -15/2

finite prefix point1 index0:original point=1;n=0;limit=14;signed coefficient=-15

f_n(x)=13/2;f_n(x)-limit=-15/2;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(-15, 3)

finite prefix point1 index1 signed correction = -5

finite prefix point1 index1 function value := sum(14, -5)

finite prefix point1 index1 function value = 9

finite prefix point1 index1 reverse signed error := sub(9, 14)

finite prefix point1 index1 reverse signed error = -5

finite prefix point1 index1:original point=1;n=1;limit=14;signed coefficient=-15

f_n(x)=9;f_n(x)-limit=-5;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(-15, 4)

finite prefix point1 index2 signed correction = -15/4

finite prefix point1 index2 function value := sum(14, -15/4)

finite prefix point1 index2 function value = 41/4

finite prefix point1 index2 reverse signed error := sub(41/4, 14)

finite prefix point1 index2 reverse signed error = -15/4

finite prefix point1 index2:original point=1;n=2;limit=14;signed coefficient=-15

f_n(x)=41/4;f_n(x)-limit=-15/4;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(-15, 5)

finite prefix point1 index3 signed correction = -3

finite prefix point1 index3 function value := sum(14, -3)

finite prefix point1 index3 function value = 11

finite prefix point1 index3 reverse signed error := sub(11, 14)

finite prefix point1 index3 reverse signed error = -3

finite prefix point1 index3:original point=1;n=3;limit=14;signed coefficient=-15

f_n(x)=11;f_n(x)-limit=-3;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(-15, 6)

finite prefix point1 index4 signed correction = -5/2

finite prefix point1 index4 function value := sum(14, -5/2)

finite prefix point1 index4 function value = 23/2

finite prefix point1 index4 reverse signed error := sub(23/2, 14)

finite prefix point1 index4 reverse signed error = -5/2

finite prefix point1 index4:original point=1;n=4;limit=14;signed coefficient=-15

f_n(x)=23/2;f_n(x)-limit=-5/2;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(-15, 7)

finite prefix point1 index5 signed correction = -15/7

finite prefix point1 index5 function value := sum(14, -15/7)

finite prefix point1 index5 function value = 83/7

finite prefix point1 index5 reverse signed error := sub(83/7, 14)

finite prefix point1 index5 reverse signed error = -15/7

finite prefix point1 index5:original point=1;n=5;limit=14;signed coefficient=-15

f_n(x)=83/7;f_n(x)-limit=-15/7;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(-15, 8)

finite prefix point1 index6 signed correction = -15/8

finite prefix point1 index6 function value := sum(14, -15/8)

finite prefix point1 index6 function value = 97/8

finite prefix point1 index6 reverse signed error := sub(97/8, 14)

finite prefix point1 index6 reverse signed error = -15/8

finite prefix point1 index6:original point=1;n=6;limit=14;signed coefficient=-15

f_n(x)=97/8;f_n(x)-limit=-15/8;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(-15, 9)

finite prefix point1 index7 signed correction = -5/3

finite prefix point1 index7 function value := sum(14, -5/3)

finite prefix point1 index7 function value = 37/3

finite prefix point1 index7 reverse signed error := sub(37/3, 14)

finite prefix point1 index7 reverse signed error = -5/3

finite prefix point1 index7:original point=1;n=7;limit=14;signed coefficient=-15

f_n(x)=37/3;f_n(x)-limit=-5/3;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(-15, 10)

finite prefix point1 index8 signed correction = -3/2

finite prefix point1 index8 function value := sum(14, -3/2)

finite prefix point1 index8 function value = 25/2

finite prefix point1 index8 reverse signed error := sub(25/2, 14)

finite prefix point1 index8 reverse signed error = -3/2

finite prefix point1 index8:original point=1;n=8;limit=14;signed coefficient=-15

f_n(x)=25/2;f_n(x)-limit=-3/2;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(-15, 11)

finite prefix point1 index9 signed correction = -15/11

finite prefix point1 index9 function value := sum(14, -15/11)

finite prefix point1 index9 function value = 139/11

finite prefix point1 index9 reverse signed error := sub(139/11, 14)

finite prefix point1 index9 reverse signed error = -15/11

finite prefix point1 index9:original point=1;n=9;limit=14;signed coefficient=-15

f_n(x)=139/11;f_n(x)-limit=-15/11;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(-15, 12)

finite prefix point1 index10 signed correction = -5/4

finite prefix point1 index10 function value := sum(14, -5/4)

finite prefix point1 index10 function value = 51/4

finite prefix point1 index10 reverse signed error := sub(51/4, 14)

finite prefix point1 index10 reverse signed error = -5/4

finite prefix point1 index10:original point=1;n=10;limit=14;signed coefficient=-15

f_n(x)=51/4;f_n(x)-limit=-5/4;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(-15, 13)

finite prefix point1 index11 signed correction = -15/13

finite prefix point1 index11 function value := sum(14, -15/13)

finite prefix point1 index11 function value = 167/13

finite prefix point1 index11 reverse signed error := sub(167/13, 14)

finite prefix point1 index11 reverse signed error = -15/13

finite prefix point1 index11:original point=1;n=11;limit=14;signed coefficient=-15

f_n(x)=167/13;f_n(x)-limit=-15/13;this error field remains SIGNED

finite prefix point1 index12 denominator := sum(12, 2)

finite prefix point1 index12 denominator = 14

finite prefix point1 index12 signed correction := div(-15, 14)

finite prefix point1 index12 signed correction = -15/14

finite prefix point1 index12 function value := sum(14, -15/14)

finite prefix point1 index12 function value = 181/14

finite prefix point1 index12 reverse signed error := sub(181/14, 14)

finite prefix point1 index12 reverse signed error = -15/14

finite prefix point1 index12:original point=1;n=12;limit=14;signed coefficient=-15

f_n(x)=181/14;f_n(x)-limit=-15/14;this error field remains SIGNED

finite prefix point1 index13 denominator := sum(13, 2)

finite prefix point1 index13 denominator = 15

finite prefix point1 index13 signed correction := div(-15, 15)

finite prefix point1 index13 signed correction = -1

finite prefix point1 index13 function value := sum(14, -1)

finite prefix point1 index13 function value = 13

finite prefix point1 index13 reverse signed error := sub(13, 14)

finite prefix point1 index13 reverse signed error = -1

finite prefix point1 index13:original point=1;n=13;limit=14;signed coefficient=-15

f_n(x)=13;f_n(x)-limit=-1;this error field remains SIGNED

finite observed length=14;complete domain-order rows=[[0, [20, 53/3, 33/2, 79/5, 46/3, 15, 59/4, 131/9, 72/5, 157/11, 85/6, 183/13, 14, 209/15]], [1, [13/2, 9, 41/4, 11, 23/2, 83/7, 97/8, 37/3, 25/2, 139/11, 51/4, 167/13, 181/14, 13]]]

prefix-alone sufficiency=否;finite_prefix_not_pointwise_convergence_certificate

逐步反向核對

• S142 · 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。
• S141 · 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。
• S140 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index13 reverse signed error，不以小數近似替代。
• S139 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index13 function value，不以小數近似替代。
• S138 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index13 signed correction，不以小數近似替代。
• S137 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index13 denominator，不以小數近似替代。
• S136 · 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。
• S135 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index12 reverse signed error，不以小數近似替代。
• S134 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index12 function value，不以小數近似替代。
• S133 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index12 signed correction，不以小數近似替代。
• S132 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index12 denominator，不以小數近似替代。
• S131 · 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。
• S130 · 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。
• S129 · 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。
• S128 · 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。
• S127 · 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。
• S126 · 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。
• S125 · 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。
• S124 · 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。
• S123 · 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。
• S122 · 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。
• 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 index9 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 index9 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 index9 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 index9 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 index8 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 index8 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 index8 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 index8 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 index7 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 index7 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 index7 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 index7 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 index6 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 index6 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 index6 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 index6 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 index5 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 index5 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 index5 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 index5 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 index4 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 index4 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 index4 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 index4 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 index3 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 index3 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 index3 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 index3 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 index2 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 index2 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 index2 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 index2 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 index1 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 index1 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 index1 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 index1 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 index0 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 index0 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 index0 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 index0 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 point0 index13 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 point0 index13 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 point0 index13 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 point0 index13 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 point0 index12 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 point0 index12 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 point0 index12 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 point0 index12 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

(14, [[0, [20, 53/3, 33/2, 79/5, 46/3, 15, 59/4, 131/9, 72/5, 157/11, 85/6, 183/13, 14, 209/15]], [1, [13/2, 9, 41/4, 11, 23/2, 83/7, 97/8, 37/3, 25/2, 139/11, 51/4, 167/13, 181/14, 13]]], 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。