第 17595 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":[19,20],"coefficients":[20,-21],"shift":2,"prefix_length":20}。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":[19,20],"coefficients":[20,-21],"shift":2,"prefix_length":20}。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=[19, 20];signed coefficients=[20, -21];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(20, 2)

finite prefix point0 index0 signed correction = 10

finite prefix point0 index0 function value := sum(19, 10)

finite prefix point0 index0 function value = 29

finite prefix point0 index0 reverse signed error := sub(29, 19)

finite prefix point0 index0 reverse signed error = 10

finite prefix point0 index0:original point=0;n=0;limit=19;signed coefficient=20

f_n(x)=29;f_n(x)-limit=10;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(20, 3)

finite prefix point0 index1 signed correction = 20/3

finite prefix point0 index1 function value := sum(19, 20/3)

finite prefix point0 index1 function value = 77/3

finite prefix point0 index1 reverse signed error := sub(77/3, 19)

finite prefix point0 index1 reverse signed error = 20/3

finite prefix point0 index1:original point=0;n=1;limit=19;signed coefficient=20

f_n(x)=77/3;f_n(x)-limit=20/3;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(20, 4)

finite prefix point0 index2 signed correction = 5

finite prefix point0 index2 function value := sum(19, 5)

finite prefix point0 index2 function value = 24

finite prefix point0 index2 reverse signed error := sub(24, 19)

finite prefix point0 index2 reverse signed error = 5

finite prefix point0 index2:original point=0;n=2;limit=19;signed coefficient=20

f_n(x)=24;f_n(x)-limit=5;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(20, 5)

finite prefix point0 index3 signed correction = 4

finite prefix point0 index3 function value := sum(19, 4)

finite prefix point0 index3 function value = 23

finite prefix point0 index3 reverse signed error := sub(23, 19)

finite prefix point0 index3 reverse signed error = 4

finite prefix point0 index3:original point=0;n=3;limit=19;signed coefficient=20

f_n(x)=23;f_n(x)-limit=4;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(20, 6)

finite prefix point0 index4 signed correction = 10/3

finite prefix point0 index4 function value := sum(19, 10/3)

finite prefix point0 index4 function value = 67/3

finite prefix point0 index4 reverse signed error := sub(67/3, 19)

finite prefix point0 index4 reverse signed error = 10/3

finite prefix point0 index4:original point=0;n=4;limit=19;signed coefficient=20

f_n(x)=67/3;f_n(x)-limit=10/3;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(20, 7)

finite prefix point0 index5 signed correction = 20/7

finite prefix point0 index5 function value := sum(19, 20/7)

finite prefix point0 index5 function value = 153/7

finite prefix point0 index5 reverse signed error := sub(153/7, 19)

finite prefix point0 index5 reverse signed error = 20/7

finite prefix point0 index5:original point=0;n=5;limit=19;signed coefficient=20

f_n(x)=153/7;f_n(x)-limit=20/7;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(20, 8)

finite prefix point0 index6 signed correction = 5/2

finite prefix point0 index6 function value := sum(19, 5/2)

finite prefix point0 index6 function value = 43/2

finite prefix point0 index6 reverse signed error := sub(43/2, 19)

finite prefix point0 index6 reverse signed error = 5/2

finite prefix point0 index6:original point=0;n=6;limit=19;signed coefficient=20

f_n(x)=43/2;f_n(x)-limit=5/2;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(20, 9)

finite prefix point0 index7 signed correction = 20/9

finite prefix point0 index7 function value := sum(19, 20/9)

finite prefix point0 index7 function value = 191/9

finite prefix point0 index7 reverse signed error := sub(191/9, 19)

finite prefix point0 index7 reverse signed error = 20/9

finite prefix point0 index7:original point=0;n=7;limit=19;signed coefficient=20

f_n(x)=191/9;f_n(x)-limit=20/9;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(20, 10)

finite prefix point0 index8 signed correction = 2

finite prefix point0 index8 function value := sum(19, 2)

finite prefix point0 index8 function value = 21

finite prefix point0 index8 reverse signed error := sub(21, 19)

finite prefix point0 index8 reverse signed error = 2

finite prefix point0 index8:original point=0;n=8;limit=19;signed coefficient=20

f_n(x)=21;f_n(x)-limit=2;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(20, 11)

finite prefix point0 index9 signed correction = 20/11

finite prefix point0 index9 function value := sum(19, 20/11)

finite prefix point0 index9 function value = 229/11

finite prefix point0 index9 reverse signed error := sub(229/11, 19)

finite prefix point0 index9 reverse signed error = 20/11

finite prefix point0 index9:original point=0;n=9;limit=19;signed coefficient=20

f_n(x)=229/11;f_n(x)-limit=20/11;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(20, 12)

finite prefix point0 index10 signed correction = 5/3

finite prefix point0 index10 function value := sum(19, 5/3)

finite prefix point0 index10 function value = 62/3

finite prefix point0 index10 reverse signed error := sub(62/3, 19)

finite prefix point0 index10 reverse signed error = 5/3

finite prefix point0 index10:original point=0;n=10;limit=19;signed coefficient=20

f_n(x)=62/3;f_n(x)-limit=5/3;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(20, 13)

finite prefix point0 index11 signed correction = 20/13

finite prefix point0 index11 function value := sum(19, 20/13)

finite prefix point0 index11 function value = 267/13

finite prefix point0 index11 reverse signed error := sub(267/13, 19)

finite prefix point0 index11 reverse signed error = 20/13

finite prefix point0 index11:original point=0;n=11;limit=19;signed coefficient=20

f_n(x)=267/13;f_n(x)-limit=20/13;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(20, 14)

finite prefix point0 index12 signed correction = 10/7

finite prefix point0 index12 function value := sum(19, 10/7)

finite prefix point0 index12 function value = 143/7

finite prefix point0 index12 reverse signed error := sub(143/7, 19)

finite prefix point0 index12 reverse signed error = 10/7

finite prefix point0 index12:original point=0;n=12;limit=19;signed coefficient=20

f_n(x)=143/7;f_n(x)-limit=10/7;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(20, 15)

finite prefix point0 index13 signed correction = 4/3

finite prefix point0 index13 function value := sum(19, 4/3)

finite prefix point0 index13 function value = 61/3

finite prefix point0 index13 reverse signed error := sub(61/3, 19)

finite prefix point0 index13 reverse signed error = 4/3

finite prefix point0 index13:original point=0;n=13;limit=19;signed coefficient=20

f_n(x)=61/3;f_n(x)-limit=4/3;this error field remains SIGNED

finite prefix point0 index14 denominator := sum(14, 2)

finite prefix point0 index14 denominator = 16

finite prefix point0 index14 signed correction := div(20, 16)

finite prefix point0 index14 signed correction = 5/4

finite prefix point0 index14 function value := sum(19, 5/4)

finite prefix point0 index14 function value = 81/4

finite prefix point0 index14 reverse signed error := sub(81/4, 19)

finite prefix point0 index14 reverse signed error = 5/4

finite prefix point0 index14:original point=0;n=14;limit=19;signed coefficient=20

f_n(x)=81/4;f_n(x)-limit=5/4;this error field remains SIGNED

finite prefix point0 index15 denominator := sum(15, 2)

finite prefix point0 index15 denominator = 17

finite prefix point0 index15 signed correction := div(20, 17)

finite prefix point0 index15 signed correction = 20/17

finite prefix point0 index15 function value := sum(19, 20/17)

finite prefix point0 index15 function value = 343/17

finite prefix point0 index15 reverse signed error := sub(343/17, 19)

finite prefix point0 index15 reverse signed error = 20/17

finite prefix point0 index15:original point=0;n=15;limit=19;signed coefficient=20

f_n(x)=343/17;f_n(x)-limit=20/17;this error field remains SIGNED

finite prefix point0 index16 denominator := sum(16, 2)

finite prefix point0 index16 denominator = 18

finite prefix point0 index16 signed correction := div(20, 18)

finite prefix point0 index16 signed correction = 10/9

finite prefix point0 index16 function value := sum(19, 10/9)

finite prefix point0 index16 function value = 181/9

finite prefix point0 index16 reverse signed error := sub(181/9, 19)

finite prefix point0 index16 reverse signed error = 10/9

finite prefix point0 index16:original point=0;n=16;limit=19;signed coefficient=20

f_n(x)=181/9;f_n(x)-limit=10/9;this error field remains SIGNED

finite prefix point0 index17 denominator := sum(17, 2)

finite prefix point0 index17 denominator = 19

finite prefix point0 index17 signed correction := div(20, 19)

finite prefix point0 index17 signed correction = 20/19

finite prefix point0 index17 function value := sum(19, 20/19)

finite prefix point0 index17 function value = 381/19

finite prefix point0 index17 reverse signed error := sub(381/19, 19)

finite prefix point0 index17 reverse signed error = 20/19

finite prefix point0 index17:original point=0;n=17;limit=19;signed coefficient=20

f_n(x)=381/19;f_n(x)-limit=20/19;this error field remains SIGNED

finite prefix point0 index18 denominator := sum(18, 2)

finite prefix point0 index18 denominator = 20

finite prefix point0 index18 signed correction := div(20, 20)

finite prefix point0 index18 signed correction = 1

finite prefix point0 index18 function value := sum(19, 1)

finite prefix point0 index18 function value = 20

finite prefix point0 index18 reverse signed error := sub(20, 19)

finite prefix point0 index18 reverse signed error = 1

finite prefix point0 index18:original point=0;n=18;limit=19;signed coefficient=20

f_n(x)=20;f_n(x)-limit=1;this error field remains SIGNED

finite prefix point0 index19 denominator := sum(19, 2)

finite prefix point0 index19 denominator = 21

finite prefix point0 index19 signed correction := div(20, 21)

finite prefix point0 index19 signed correction = 20/21

finite prefix point0 index19 function value := sum(19, 20/21)

finite prefix point0 index19 function value = 419/21

finite prefix point0 index19 reverse signed error := sub(419/21, 19)

finite prefix point0 index19 reverse signed error = 20/21

finite prefix point0 index19:original point=0;n=19;limit=19;signed coefficient=20

f_n(x)=419/21;f_n(x)-limit=20/21;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(-21, 2)

finite prefix point1 index0 signed correction = -21/2

finite prefix point1 index0 function value := sum(20, -21/2)

finite prefix point1 index0 function value = 19/2

finite prefix point1 index0 reverse signed error := sub(19/2, 20)

finite prefix point1 index0 reverse signed error = -21/2

finite prefix point1 index0:original point=1;n=0;limit=20;signed coefficient=-21

f_n(x)=19/2;f_n(x)-limit=-21/2;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(-21, 3)

finite prefix point1 index1 signed correction = -7

finite prefix point1 index1 function value := sum(20, -7)

finite prefix point1 index1 function value = 13

finite prefix point1 index1 reverse signed error := sub(13, 20)

finite prefix point1 index1 reverse signed error = -7

finite prefix point1 index1:original point=1;n=1;limit=20;signed coefficient=-21

f_n(x)=13;f_n(x)-limit=-7;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(-21, 4)

finite prefix point1 index2 signed correction = -21/4

finite prefix point1 index2 function value := sum(20, -21/4)

finite prefix point1 index2 function value = 59/4

finite prefix point1 index2 reverse signed error := sub(59/4, 20)

finite prefix point1 index2 reverse signed error = -21/4

finite prefix point1 index2:original point=1;n=2;limit=20;signed coefficient=-21

f_n(x)=59/4;f_n(x)-limit=-21/4;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(-21, 5)

finite prefix point1 index3 signed correction = -21/5

finite prefix point1 index3 function value := sum(20, -21/5)

finite prefix point1 index3 function value = 79/5

finite prefix point1 index3 reverse signed error := sub(79/5, 20)

finite prefix point1 index3 reverse signed error = -21/5

finite prefix point1 index3:original point=1;n=3;limit=20;signed coefficient=-21

f_n(x)=79/5;f_n(x)-limit=-21/5;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(-21, 6)

finite prefix point1 index4 signed correction = -7/2

finite prefix point1 index4 function value := sum(20, -7/2)

finite prefix point1 index4 function value = 33/2

finite prefix point1 index4 reverse signed error := sub(33/2, 20)

finite prefix point1 index4 reverse signed error = -7/2

finite prefix point1 index4:original point=1;n=4;limit=20;signed coefficient=-21

f_n(x)=33/2;f_n(x)-limit=-7/2;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(-21, 7)

finite prefix point1 index5 signed correction = -3

finite prefix point1 index5 function value := sum(20, -3)

finite prefix point1 index5 function value = 17

finite prefix point1 index5 reverse signed error := sub(17, 20)

finite prefix point1 index5 reverse signed error = -3

finite prefix point1 index5:original point=1;n=5;limit=20;signed coefficient=-21

f_n(x)=17;f_n(x)-limit=-3;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(-21, 8)

finite prefix point1 index6 signed correction = -21/8

finite prefix point1 index6 function value := sum(20, -21/8)

finite prefix point1 index6 function value = 139/8

finite prefix point1 index6 reverse signed error := sub(139/8, 20)

finite prefix point1 index6 reverse signed error = -21/8

finite prefix point1 index6:original point=1;n=6;limit=20;signed coefficient=-21

f_n(x)=139/8;f_n(x)-limit=-21/8;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(-21, 9)

finite prefix point1 index7 signed correction = -7/3

finite prefix point1 index7 function value := sum(20, -7/3)

finite prefix point1 index7 function value = 53/3

finite prefix point1 index7 reverse signed error := sub(53/3, 20)

finite prefix point1 index7 reverse signed error = -7/3

finite prefix point1 index7:original point=1;n=7;limit=20;signed coefficient=-21

f_n(x)=53/3;f_n(x)-limit=-7/3;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(-21, 10)

finite prefix point1 index8 signed correction = -21/10

finite prefix point1 index8 function value := sum(20, -21/10)

finite prefix point1 index8 function value = 179/10

finite prefix point1 index8 reverse signed error := sub(179/10, 20)

finite prefix point1 index8 reverse signed error = -21/10

finite prefix point1 index8:original point=1;n=8;limit=20;signed coefficient=-21

f_n(x)=179/10;f_n(x)-limit=-21/10;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(-21, 11)

finite prefix point1 index9 signed correction = -21/11

finite prefix point1 index9 function value := sum(20, -21/11)

finite prefix point1 index9 function value = 199/11

finite prefix point1 index9 reverse signed error := sub(199/11, 20)

finite prefix point1 index9 reverse signed error = -21/11

finite prefix point1 index9:original point=1;n=9;limit=20;signed coefficient=-21

f_n(x)=199/11;f_n(x)-limit=-21/11;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(-21, 12)

finite prefix point1 index10 signed correction = -7/4

finite prefix point1 index10 function value := sum(20, -7/4)

finite prefix point1 index10 function value = 73/4

finite prefix point1 index10 reverse signed error := sub(73/4, 20)

finite prefix point1 index10 reverse signed error = -7/4

finite prefix point1 index10:original point=1;n=10;limit=20;signed coefficient=-21

f_n(x)=73/4;f_n(x)-limit=-7/4;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(-21, 13)

finite prefix point1 index11 signed correction = -21/13

finite prefix point1 index11 function value := sum(20, -21/13)

finite prefix point1 index11 function value = 239/13

finite prefix point1 index11 reverse signed error := sub(239/13, 20)

finite prefix point1 index11 reverse signed error = -21/13

finite prefix point1 index11:original point=1;n=11;limit=20;signed coefficient=-21

f_n(x)=239/13;f_n(x)-limit=-21/13;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(-21, 14)

finite prefix point1 index12 signed correction = -3/2

finite prefix point1 index12 function value := sum(20, -3/2)

finite prefix point1 index12 function value = 37/2

finite prefix point1 index12 reverse signed error := sub(37/2, 20)

finite prefix point1 index12 reverse signed error = -3/2

finite prefix point1 index12:original point=1;n=12;limit=20;signed coefficient=-21

f_n(x)=37/2;f_n(x)-limit=-3/2;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(-21, 15)

finite prefix point1 index13 signed correction = -7/5

finite prefix point1 index13 function value := sum(20, -7/5)

finite prefix point1 index13 function value = 93/5

finite prefix point1 index13 reverse signed error := sub(93/5, 20)

finite prefix point1 index13 reverse signed error = -7/5

finite prefix point1 index13:original point=1;n=13;limit=20;signed coefficient=-21

f_n(x)=93/5;f_n(x)-limit=-7/5;this error field remains SIGNED

finite prefix point1 index14 denominator := sum(14, 2)

finite prefix point1 index14 denominator = 16

finite prefix point1 index14 signed correction := div(-21, 16)

finite prefix point1 index14 signed correction = -21/16

finite prefix point1 index14 function value := sum(20, -21/16)

finite prefix point1 index14 function value = 299/16

finite prefix point1 index14 reverse signed error := sub(299/16, 20)

finite prefix point1 index14 reverse signed error = -21/16

finite prefix point1 index14:original point=1;n=14;limit=20;signed coefficient=-21

f_n(x)=299/16;f_n(x)-limit=-21/16;this error field remains SIGNED

finite prefix point1 index15 denominator := sum(15, 2)

finite prefix point1 index15 denominator = 17

finite prefix point1 index15 signed correction := div(-21, 17)

finite prefix point1 index15 signed correction = -21/17

finite prefix point1 index15 function value := sum(20, -21/17)

finite prefix point1 index15 function value = 319/17

finite prefix point1 index15 reverse signed error := sub(319/17, 20)

finite prefix point1 index15 reverse signed error = -21/17

finite prefix point1 index15:original point=1;n=15;limit=20;signed coefficient=-21

f_n(x)=319/17;f_n(x)-limit=-21/17;this error field remains SIGNED

finite prefix point1 index16 denominator := sum(16, 2)

finite prefix point1 index16 denominator = 18

finite prefix point1 index16 signed correction := div(-21, 18)

finite prefix point1 index16 signed correction = -7/6

finite prefix point1 index16 function value := sum(20, -7/6)

finite prefix point1 index16 function value = 113/6

finite prefix point1 index16 reverse signed error := sub(113/6, 20)

finite prefix point1 index16 reverse signed error = -7/6

finite prefix point1 index16:original point=1;n=16;limit=20;signed coefficient=-21

f_n(x)=113/6;f_n(x)-limit=-7/6;this error field remains SIGNED

finite prefix point1 index17 denominator := sum(17, 2)

finite prefix point1 index17 denominator = 19

finite prefix point1 index17 signed correction := div(-21, 19)

finite prefix point1 index17 signed correction = -21/19

finite prefix point1 index17 function value := sum(20, -21/19)

finite prefix point1 index17 function value = 359/19

finite prefix point1 index17 reverse signed error := sub(359/19, 20)

finite prefix point1 index17 reverse signed error = -21/19

finite prefix point1 index17:original point=1;n=17;limit=20;signed coefficient=-21

f_n(x)=359/19;f_n(x)-limit=-21/19;this error field remains SIGNED

finite prefix point1 index18 denominator := sum(18, 2)

finite prefix point1 index18 denominator = 20

finite prefix point1 index18 signed correction := div(-21, 20)

finite prefix point1 index18 signed correction = -21/20

finite prefix point1 index18 function value := sum(20, -21/20)

finite prefix point1 index18 function value = 379/20

finite prefix point1 index18 reverse signed error := sub(379/20, 20)

finite prefix point1 index18 reverse signed error = -21/20

finite prefix point1 index18:original point=1;n=18;limit=20;signed coefficient=-21

f_n(x)=379/20;f_n(x)-limit=-21/20;this error field remains SIGNED

finite prefix point1 index19 denominator := sum(19, 2)

finite prefix point1 index19 denominator = 21

finite prefix point1 index19 signed correction := div(-21, 21)

finite prefix point1 index19 signed correction = -1

finite prefix point1 index19 function value := sum(20, -1)

finite prefix point1 index19 function value = 19

finite prefix point1 index19 reverse signed error := sub(19, 20)

finite prefix point1 index19 reverse signed error = -1

finite prefix point1 index19:original point=1;n=19;limit=20;signed coefficient=-21

f_n(x)=19;f_n(x)-limit=-1;this error field remains SIGNED

finite observed length=20;complete domain-order rows=[[0, [29, 77/3, 24, 23, 67/3, 153/7, 43/2, 191/9, 21, 229/11, 62/3, 267/13, 143/7, 61/3, 81/4, 343/17, 181/9, 381/19, 20, 419/21]], [1, [19/2, 13, 59/4, 79/5, 33/2, 17, 139/8, 53/3, 179/10, 199/11, 73/4, 239/13, 37/2, 93/5, 299/16, 319/17, 113/6, 359/19, 379/20, 19]]]

prefix-alone sufficiency=否;finite_prefix_not_pointwise_convergence_certificate

逐步反向核對

• S202 · 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。
• S201 · 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。
• S200 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index19 reverse signed error，不以小數近似替代。
• S199 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index19 function value，不以小數近似替代。
• S198 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index19 signed correction，不以小數近似替代。
• S197 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index19 denominator，不以小數近似替代。
• S196 · 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。
• S195 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index18 reverse signed error，不以小數近似替代。
• S194 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index18 function value，不以小數近似替代。
• S193 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index18 signed correction，不以小數近似替代。
• S192 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index18 denominator，不以小數近似替代。
• S191 · 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。
• S190 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index17 reverse signed error，不以小數近似替代。
• S189 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index17 function value，不以小數近似替代。
• S188 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index17 signed correction，不以小數近似替代。
• S187 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index17 denominator，不以小數近似替代。
• S186 · 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。
• S185 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index16 reverse signed error，不以小數近似替代。
• S184 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index16 function value，不以小數近似替代。
• S183 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index16 signed correction，不以小數近似替代。
• S182 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index16 denominator，不以小數近似替代。
• S181 · 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。
• S180 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index15 reverse signed error，不以小數近似替代。
• S179 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index15 function value，不以小數近似替代。
• S178 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index15 signed correction，不以小數近似替代。
• S177 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index15 denominator，不以小數近似替代。
• S176 · 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。
• S175 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index14 reverse signed error，不以小數近似替代。
• S174 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index14 function value，不以小數近似替代。
• S173 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index14 signed correction，不以小數近似替代。
• S172 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index14 denominator，不以小數近似替代。
• S171 · 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。
• S170 · 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。
• S169 · 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。
• S168 · 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。
• S167 · 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。
• S166 · 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。
• S165 · 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。
• S164 · 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。
• S163 · 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。
• S162 · 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。
• S161 · 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。
• S160 · 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。
• S159 · 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。
• S158 · 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。
• S157 · 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。
• S156 · 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。
• S155 · 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。
• S154 · 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。
• S153 · 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。
• S152 · 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。
• S151 · 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。
• S150 · 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。
• S149 · 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。
• S148 · 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。
• S147 · 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。
• S146 · 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。
• S145 · 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。
• S144 · 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。
• S143 · 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。
• S142 · 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。
• 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 index7 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 index7 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 index7 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 index7 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 index6 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 index6 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 index6 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 index6 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 index5 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 index5 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 index5 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 index5 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 index4 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 index4 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 index4 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 index4 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 index3 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 index3 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 index3 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 index3 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 index2 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 index2 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 index2 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 index2 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 index1 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 index1 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 index1 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 index1 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 index0 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 index0 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 index0 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 index0 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 point0 index19 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 point0 index19 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 point0 index19 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 point0 index19 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 point0 index18 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 point0 index18 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 point0 index18 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 point0 index18 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 point0 index17 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 point0 index17 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 point0 index17 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 point0 index17 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 point0 index16 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 point0 index16 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 point0 index16 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 point0 index16 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 point0 index15 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 point0 index15 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 point0 index15 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 point0 index15 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 point0 index14 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 point0 index14 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 point0 index14 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 point0 index14 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

(20, [[0, [29, 77/3, 24, 23, 67/3, 153/7, 43/2, 191/9, 21, 229/11, 62/3, 267/13, 143/7, 61/3, 81/4, 343/17, 181/9, 381/19, 20, 419/21]], [1, [19/2, 13, 59/4, 79/5, 33/2, 17, 139/8, 53/3, 179/10, 199/11, 73/4, 239/13, 37/2, 93/5, 299/16, 319/17, 113/6, 359/19, 379/20, 19]]], 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。