第 32620 題：仿射式的左端有限和

原題與已知條件

全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-20x+(7)，區間 [1,6] 分為 N=20 等份。求左端有限和 ΔΣ f(a+iΔ)，i=0至N−1、Δ=(b−a)/N。

• G001 — 全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-20x+(7)，區間 [1,6] 分為 N=20 等份。求左端有限和 ΔΣ f(a+iΔ)，i=0至N−1、Δ=(b−a)/N。

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-definite-integral

逐步推導

source roles = [qf-integral-affine-left-sum, affine_left_sum, reals, []]

derived = [[finite_left_sum_fraction_RETAIN1]]

Left sum ORIGINAL upper minus lower endpoint := sub(6, 1)

Left sum ORIGINAL upper minus lower endpoint = 5

Left sum ORIGINAL width over positive cell count := div(5, 20)

Left sum ORIGINAL width over positive cell count = 1/4

Left sum ORIGINAL sample0 index times width := mul(0, 1/4)

Left sum ORIGINAL sample0 index times width = 0

Left sum ORIGINAL sample0 lower plus offset := sum(1, 0)

Left sum ORIGINAL sample0 lower plus offset = 1

Left sum ORIGINAL sample0 slope times x := mul(-20, 1)

Left sum ORIGINAL sample0 slope times x = -20

Left sum ORIGINAL sample0 affine value plus c := sum(-20, 7)

Left sum ORIGINAL sample0 affine value plus c = -13

Left sum ORIGINAL sample0 value times cell width := mul(-13, 1/4)

Left sum ORIGINAL sample0 value times cell width = -13/4

Left sum ORIGINAL accumulated term0 := sum(0, -13/4)

Left sum ORIGINAL accumulated term0 = -13/4

source roles = [0, 20, -20, 7, 1, 6, 1/4]

derived = [1/1, -13/1, -13/4, -13/4]

Left sum ORIGINAL sample1 index times width := mul(1, 1/4)

Left sum ORIGINAL sample1 index times width = 1/4

Left sum ORIGINAL sample1 lower plus offset := sum(1, 1/4)

Left sum ORIGINAL sample1 lower plus offset = 5/4

Left sum ORIGINAL sample1 slope times x := mul(-20, 5/4)

Left sum ORIGINAL sample1 slope times x = -25

Left sum ORIGINAL sample1 affine value plus c := sum(-25, 7)

Left sum ORIGINAL sample1 affine value plus c = -18

Left sum ORIGINAL sample1 value times cell width := mul(-18, 1/4)

Left sum ORIGINAL sample1 value times cell width = -9/2

Left sum ORIGINAL accumulated term1 := sum(-13/4, -9/2)

Left sum ORIGINAL accumulated term1 = -31/4

source roles = [1, 20, -20, 7, 1, 6, 1/4]

derived = [5/4, -18/1, -9/2, -31/4]

Left sum ORIGINAL sample2 index times width := mul(2, 1/4)

Left sum ORIGINAL sample2 index times width = 1/2

Left sum ORIGINAL sample2 lower plus offset := sum(1, 1/2)

Left sum ORIGINAL sample2 lower plus offset = 3/2

Left sum ORIGINAL sample2 slope times x := mul(-20, 3/2)

Left sum ORIGINAL sample2 slope times x = -30

Left sum ORIGINAL sample2 affine value plus c := sum(-30, 7)

Left sum ORIGINAL sample2 affine value plus c = -23

Left sum ORIGINAL sample2 value times cell width := mul(-23, 1/4)

Left sum ORIGINAL sample2 value times cell width = -23/4

Left sum ORIGINAL accumulated term2 := sum(-31/4, -23/4)

Left sum ORIGINAL accumulated term2 = -27/2

source roles = [2, 20, -20, 7, 1, 6, 1/4]

derived = [3/2, -23/1, -23/4, -27/2]

Left sum ORIGINAL sample3 index times width := mul(3, 1/4)

Left sum ORIGINAL sample3 index times width = 3/4

Left sum ORIGINAL sample3 lower plus offset := sum(1, 3/4)

Left sum ORIGINAL sample3 lower plus offset = 7/4

Left sum ORIGINAL sample3 slope times x := mul(-20, 7/4)

Left sum ORIGINAL sample3 slope times x = -35

Left sum ORIGINAL sample3 affine value plus c := sum(-35, 7)

Left sum ORIGINAL sample3 affine value plus c = -28

Left sum ORIGINAL sample3 value times cell width := mul(-28, 1/4)

Left sum ORIGINAL sample3 value times cell width = -7

Left sum ORIGINAL accumulated term3 := sum(-27/2, -7)

Left sum ORIGINAL accumulated term3 = -41/2

source roles = [3, 20, -20, 7, 1, 6, 1/4]

derived = [7/4, -28/1, -7/1, -41/2]

Left sum ORIGINAL sample4 index times width := mul(4, 1/4)

Left sum ORIGINAL sample4 index times width = 1

Left sum ORIGINAL sample4 lower plus offset := sum(1, 1)

Left sum ORIGINAL sample4 lower plus offset = 2

Left sum ORIGINAL sample4 slope times x := mul(-20, 2)

Left sum ORIGINAL sample4 slope times x = -40

Left sum ORIGINAL sample4 affine value plus c := sum(-40, 7)

Left sum ORIGINAL sample4 affine value plus c = -33

Left sum ORIGINAL sample4 value times cell width := mul(-33, 1/4)

Left sum ORIGINAL sample4 value times cell width = -33/4

Left sum ORIGINAL accumulated term4 := sum(-41/2, -33/4)

Left sum ORIGINAL accumulated term4 = -115/4

source roles = [4, 20, -20, 7, 1, 6, 1/4]

derived = [2/1, -33/1, -33/4, -115/4]

Left sum ORIGINAL sample5 index times width := mul(5, 1/4)

Left sum ORIGINAL sample5 index times width = 5/4

Left sum ORIGINAL sample5 lower plus offset := sum(1, 5/4)

Left sum ORIGINAL sample5 lower plus offset = 9/4

Left sum ORIGINAL sample5 slope times x := mul(-20, 9/4)

Left sum ORIGINAL sample5 slope times x = -45

Left sum ORIGINAL sample5 affine value plus c := sum(-45, 7)

Left sum ORIGINAL sample5 affine value plus c = -38

Left sum ORIGINAL sample5 value times cell width := mul(-38, 1/4)

Left sum ORIGINAL sample5 value times cell width = -19/2

Left sum ORIGINAL accumulated term5 := sum(-115/4, -19/2)

Left sum ORIGINAL accumulated term5 = -153/4

source roles = [5, 20, -20, 7, 1, 6, 1/4]

derived = [9/4, -38/1, -19/2, -153/4]

Left sum ORIGINAL sample6 index times width := mul(6, 1/4)

Left sum ORIGINAL sample6 index times width = 3/2

Left sum ORIGINAL sample6 lower plus offset := sum(1, 3/2)

Left sum ORIGINAL sample6 lower plus offset = 5/2

Left sum ORIGINAL sample6 slope times x := mul(-20, 5/2)

Left sum ORIGINAL sample6 slope times x = -50

Left sum ORIGINAL sample6 affine value plus c := sum(-50, 7)

Left sum ORIGINAL sample6 affine value plus c = -43

Left sum ORIGINAL sample6 value times cell width := mul(-43, 1/4)

Left sum ORIGINAL sample6 value times cell width = -43/4

Left sum ORIGINAL accumulated term6 := sum(-153/4, -43/4)

Left sum ORIGINAL accumulated term6 = -49

source roles = [6, 20, -20, 7, 1, 6, 1/4]

derived = [5/2, -43/1, -43/4, -49/1]

Left sum ORIGINAL sample7 index times width := mul(7, 1/4)

Left sum ORIGINAL sample7 index times width = 7/4

Left sum ORIGINAL sample7 lower plus offset := sum(1, 7/4)

Left sum ORIGINAL sample7 lower plus offset = 11/4

Left sum ORIGINAL sample7 slope times x := mul(-20, 11/4)

Left sum ORIGINAL sample7 slope times x = -55

Left sum ORIGINAL sample7 affine value plus c := sum(-55, 7)

Left sum ORIGINAL sample7 affine value plus c = -48

Left sum ORIGINAL sample7 value times cell width := mul(-48, 1/4)

Left sum ORIGINAL sample7 value times cell width = -12

Left sum ORIGINAL accumulated term7 := sum(-49, -12)

Left sum ORIGINAL accumulated term7 = -61

source roles = [7, 20, -20, 7, 1, 6, 1/4]

derived = [11/4, -48/1, -12/1, -61/1]

Left sum ORIGINAL sample8 index times width := mul(8, 1/4)

Left sum ORIGINAL sample8 index times width = 2

Left sum ORIGINAL sample8 lower plus offset := sum(1, 2)

Left sum ORIGINAL sample8 lower plus offset = 3

Left sum ORIGINAL sample8 slope times x := mul(-20, 3)

Left sum ORIGINAL sample8 slope times x = -60

Left sum ORIGINAL sample8 affine value plus c := sum(-60, 7)

Left sum ORIGINAL sample8 affine value plus c = -53

Left sum ORIGINAL sample8 value times cell width := mul(-53, 1/4)

Left sum ORIGINAL sample8 value times cell width = -53/4

Left sum ORIGINAL accumulated term8 := sum(-61, -53/4)

Left sum ORIGINAL accumulated term8 = -297/4

source roles = [8, 20, -20, 7, 1, 6, 1/4]

derived = [3/1, -53/1, -53/4, -297/4]

Left sum ORIGINAL sample9 index times width := mul(9, 1/4)

Left sum ORIGINAL sample9 index times width = 9/4

Left sum ORIGINAL sample9 lower plus offset := sum(1, 9/4)

Left sum ORIGINAL sample9 lower plus offset = 13/4

Left sum ORIGINAL sample9 slope times x := mul(-20, 13/4)

Left sum ORIGINAL sample9 slope times x = -65

Left sum ORIGINAL sample9 affine value plus c := sum(-65, 7)

Left sum ORIGINAL sample9 affine value plus c = -58

Left sum ORIGINAL sample9 value times cell width := mul(-58, 1/4)

Left sum ORIGINAL sample9 value times cell width = -29/2

Left sum ORIGINAL accumulated term9 := sum(-297/4, -29/2)

Left sum ORIGINAL accumulated term9 = -355/4

source roles = [9, 20, -20, 7, 1, 6, 1/4]

derived = [13/4, -58/1, -29/2, -355/4]

Left sum ORIGINAL sample10 index times width := mul(10, 1/4)

Left sum ORIGINAL sample10 index times width = 5/2

Left sum ORIGINAL sample10 lower plus offset := sum(1, 5/2)

Left sum ORIGINAL sample10 lower plus offset = 7/2

Left sum ORIGINAL sample10 slope times x := mul(-20, 7/2)

Left sum ORIGINAL sample10 slope times x = -70

Left sum ORIGINAL sample10 affine value plus c := sum(-70, 7)

Left sum ORIGINAL sample10 affine value plus c = -63

Left sum ORIGINAL sample10 value times cell width := mul(-63, 1/4)

Left sum ORIGINAL sample10 value times cell width = -63/4

Left sum ORIGINAL accumulated term10 := sum(-355/4, -63/4)

Left sum ORIGINAL accumulated term10 = -209/2

source roles = [10, 20, -20, 7, 1, 6, 1/4]

derived = [7/2, -63/1, -63/4, -209/2]

Left sum ORIGINAL sample11 index times width := mul(11, 1/4)

Left sum ORIGINAL sample11 index times width = 11/4

Left sum ORIGINAL sample11 lower plus offset := sum(1, 11/4)

Left sum ORIGINAL sample11 lower plus offset = 15/4

Left sum ORIGINAL sample11 slope times x := mul(-20, 15/4)

Left sum ORIGINAL sample11 slope times x = -75

Left sum ORIGINAL sample11 affine value plus c := sum(-75, 7)

Left sum ORIGINAL sample11 affine value plus c = -68

Left sum ORIGINAL sample11 value times cell width := mul(-68, 1/4)

Left sum ORIGINAL sample11 value times cell width = -17

Left sum ORIGINAL accumulated term11 := sum(-209/2, -17)

Left sum ORIGINAL accumulated term11 = -243/2

source roles = [11, 20, -20, 7, 1, 6, 1/4]

derived = [15/4, -68/1, -17/1, -243/2]

Left sum ORIGINAL sample12 index times width := mul(12, 1/4)

Left sum ORIGINAL sample12 index times width = 3

Left sum ORIGINAL sample12 lower plus offset := sum(1, 3)

Left sum ORIGINAL sample12 lower plus offset = 4

Left sum ORIGINAL sample12 slope times x := mul(-20, 4)

Left sum ORIGINAL sample12 slope times x = -80

Left sum ORIGINAL sample12 affine value plus c := sum(-80, 7)

Left sum ORIGINAL sample12 affine value plus c = -73

Left sum ORIGINAL sample12 value times cell width := mul(-73, 1/4)

Left sum ORIGINAL sample12 value times cell width = -73/4

Left sum ORIGINAL accumulated term12 := sum(-243/2, -73/4)

Left sum ORIGINAL accumulated term12 = -559/4

source roles = [12, 20, -20, 7, 1, 6, 1/4]

derived = [4/1, -73/1, -73/4, -559/4]

Left sum ORIGINAL sample13 index times width := mul(13, 1/4)

Left sum ORIGINAL sample13 index times width = 13/4

Left sum ORIGINAL sample13 lower plus offset := sum(1, 13/4)

Left sum ORIGINAL sample13 lower plus offset = 17/4

Left sum ORIGINAL sample13 slope times x := mul(-20, 17/4)

Left sum ORIGINAL sample13 slope times x = -85

Left sum ORIGINAL sample13 affine value plus c := sum(-85, 7)

Left sum ORIGINAL sample13 affine value plus c = -78

Left sum ORIGINAL sample13 value times cell width := mul(-78, 1/4)

Left sum ORIGINAL sample13 value times cell width = -39/2

Left sum ORIGINAL accumulated term13 := sum(-559/4, -39/2)

Left sum ORIGINAL accumulated term13 = -637/4

source roles = [13, 20, -20, 7, 1, 6, 1/4]

derived = [17/4, -78/1, -39/2, -637/4]

Left sum ORIGINAL sample14 index times width := mul(14, 1/4)

Left sum ORIGINAL sample14 index times width = 7/2

Left sum ORIGINAL sample14 lower plus offset := sum(1, 7/2)

Left sum ORIGINAL sample14 lower plus offset = 9/2

Left sum ORIGINAL sample14 slope times x := mul(-20, 9/2)

Left sum ORIGINAL sample14 slope times x = -90

Left sum ORIGINAL sample14 affine value plus c := sum(-90, 7)

Left sum ORIGINAL sample14 affine value plus c = -83

Left sum ORIGINAL sample14 value times cell width := mul(-83, 1/4)

Left sum ORIGINAL sample14 value times cell width = -83/4

Left sum ORIGINAL accumulated term14 := sum(-637/4, -83/4)

Left sum ORIGINAL accumulated term14 = -180

source roles = [14, 20, -20, 7, 1, 6, 1/4]

derived = [9/2, -83/1, -83/4, -180/1]

Left sum ORIGINAL sample15 index times width := mul(15, 1/4)

Left sum ORIGINAL sample15 index times width = 15/4

Left sum ORIGINAL sample15 lower plus offset := sum(1, 15/4)

Left sum ORIGINAL sample15 lower plus offset = 19/4

Left sum ORIGINAL sample15 slope times x := mul(-20, 19/4)

Left sum ORIGINAL sample15 slope times x = -95

Left sum ORIGINAL sample15 affine value plus c := sum(-95, 7)

Left sum ORIGINAL sample15 affine value plus c = -88

Left sum ORIGINAL sample15 value times cell width := mul(-88, 1/4)

Left sum ORIGINAL sample15 value times cell width = -22

Left sum ORIGINAL accumulated term15 := sum(-180, -22)

Left sum ORIGINAL accumulated term15 = -202

source roles = [15, 20, -20, 7, 1, 6, 1/4]

derived = [19/4, -88/1, -22/1, -202/1]

Left sum ORIGINAL sample16 index times width := mul(16, 1/4)

Left sum ORIGINAL sample16 index times width = 4

Left sum ORIGINAL sample16 lower plus offset := sum(1, 4)

Left sum ORIGINAL sample16 lower plus offset = 5

Left sum ORIGINAL sample16 slope times x := mul(-20, 5)

Left sum ORIGINAL sample16 slope times x = -100

Left sum ORIGINAL sample16 affine value plus c := sum(-100, 7)

Left sum ORIGINAL sample16 affine value plus c = -93

Left sum ORIGINAL sample16 value times cell width := mul(-93, 1/4)

Left sum ORIGINAL sample16 value times cell width = -93/4

Left sum ORIGINAL accumulated term16 := sum(-202, -93/4)

Left sum ORIGINAL accumulated term16 = -901/4

source roles = [16, 20, -20, 7, 1, 6, 1/4]

derived = [5/1, -93/1, -93/4, -901/4]

Left sum ORIGINAL sample17 index times width := mul(17, 1/4)

Left sum ORIGINAL sample17 index times width = 17/4

Left sum ORIGINAL sample17 lower plus offset := sum(1, 17/4)

Left sum ORIGINAL sample17 lower plus offset = 21/4

Left sum ORIGINAL sample17 slope times x := mul(-20, 21/4)

Left sum ORIGINAL sample17 slope times x = -105

Left sum ORIGINAL sample17 affine value plus c := sum(-105, 7)

Left sum ORIGINAL sample17 affine value plus c = -98

Left sum ORIGINAL sample17 value times cell width := mul(-98, 1/4)

Left sum ORIGINAL sample17 value times cell width = -49/2

Left sum ORIGINAL accumulated term17 := sum(-901/4, -49/2)

Left sum ORIGINAL accumulated term17 = -999/4

source roles = [17, 20, -20, 7, 1, 6, 1/4]

derived = [21/4, -98/1, -49/2, -999/4]

Left sum ORIGINAL sample18 index times width := mul(18, 1/4)

Left sum ORIGINAL sample18 index times width = 9/2

Left sum ORIGINAL sample18 lower plus offset := sum(1, 9/2)

Left sum ORIGINAL sample18 lower plus offset = 11/2

Left sum ORIGINAL sample18 slope times x := mul(-20, 11/2)

Left sum ORIGINAL sample18 slope times x = -110

Left sum ORIGINAL sample18 affine value plus c := sum(-110, 7)

Left sum ORIGINAL sample18 affine value plus c = -103

Left sum ORIGINAL sample18 value times cell width := mul(-103, 1/4)

Left sum ORIGINAL sample18 value times cell width = -103/4

Left sum ORIGINAL accumulated term18 := sum(-999/4, -103/4)

Left sum ORIGINAL accumulated term18 = -551/2

source roles = [18, 20, -20, 7, 1, 6, 1/4]

derived = [11/2, -103/1, -103/4, -551/2]

Left sum ORIGINAL sample19 index times width := mul(19, 1/4)

Left sum ORIGINAL sample19 index times width = 19/4

Left sum ORIGINAL sample19 lower plus offset := sum(1, 19/4)

Left sum ORIGINAL sample19 lower plus offset = 23/4

Left sum ORIGINAL sample19 slope times x := mul(-20, 23/4)

Left sum ORIGINAL sample19 slope times x = -115

Left sum ORIGINAL sample19 affine value plus c := sum(-115, 7)

Left sum ORIGINAL sample19 affine value plus c = -108

Left sum ORIGINAL sample19 value times cell width := mul(-108, 1/4)

Left sum ORIGINAL sample19 value times cell width = -27

Left sum ORIGINAL accumulated term19 := sum(-551/2, -27)

Left sum ORIGINAL accumulated term19 = -605/2

source roles = [19, 20, -20, 7, 1, 6, 1/4]

derived = [23/4, -108/1, -27/1, -605/2]

source roles = [20, -20, 7, 1, 6]

derived = [1/4, -605/2]

逐步反向核對

• S144 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S143 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S142 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term19，不以小數近似替代。
• S141 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample19 value times cell width，不以小數近似替代。
• S140 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample19 affine value plus c，不以小數近似替代。
• S139 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample19 slope times x，不以小數近似替代。
• S138 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample19 lower plus offset，不以小數近似替代。
• S137 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample19 index times width，不以小數近似替代。
• S136 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S135 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term18，不以小數近似替代。
• S134 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample18 value times cell width，不以小數近似替代。
• S133 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample18 affine value plus c，不以小數近似替代。
• S132 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample18 slope times x，不以小數近似替代。
• S131 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample18 lower plus offset，不以小數近似替代。
• S130 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample18 index times width，不以小數近似替代。
• S129 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S128 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term17，不以小數近似替代。
• S127 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample17 value times cell width，不以小數近似替代。
• S126 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample17 affine value plus c，不以小數近似替代。
• S125 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample17 slope times x，不以小數近似替代。
• S124 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample17 lower plus offset，不以小數近似替代。
• S123 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample17 index times width，不以小數近似替代。
• S122 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S121 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term16，不以小數近似替代。
• S120 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample16 value times cell width，不以小數近似替代。
• S119 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample16 affine value plus c，不以小數近似替代。
• S118 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample16 slope times x，不以小數近似替代。
• S117 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample16 lower plus offset，不以小數近似替代。
• S116 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample16 index times width，不以小數近似替代。
• S115 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S114 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term15，不以小數近似替代。
• S113 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample15 value times cell width，不以小數近似替代。
• S112 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample15 affine value plus c，不以小數近似替代。
• S111 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample15 slope times x，不以小數近似替代。
• S110 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample15 lower plus offset，不以小數近似替代。
• S109 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample15 index times width，不以小數近似替代。
• S108 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S107 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term14，不以小數近似替代。
• S106 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample14 value times cell width，不以小數近似替代。
• S105 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample14 affine value plus c，不以小數近似替代。
• S104 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample14 slope times x，不以小數近似替代。
• S103 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample14 lower plus offset，不以小數近似替代。
• S102 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample14 index times width，不以小數近似替代。
• S101 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S100 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term13，不以小數近似替代。
• S099 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample13 value times cell width，不以小數近似替代。
• S098 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample13 affine value plus c，不以小數近似替代。
• S097 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample13 slope times x，不以小數近似替代。
• S096 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample13 lower plus offset，不以小數近似替代。
• S095 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample13 index times width，不以小數近似替代。
• S094 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S093 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term12，不以小數近似替代。
• S092 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample12 value times cell width，不以小數近似替代。
• S091 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample12 affine value plus c，不以小數近似替代。
• S090 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample12 slope times x，不以小數近似替代。
• S089 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample12 lower plus offset，不以小數近似替代。
• S088 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample12 index times width，不以小數近似替代。
• S087 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S086 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term11，不以小數近似替代。
• S085 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample11 value times cell width，不以小數近似替代。
• S084 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample11 affine value plus c，不以小數近似替代。
• S083 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample11 slope times x，不以小數近似替代。
• S082 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample11 lower plus offset，不以小數近似替代。
• S081 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample11 index times width，不以小數近似替代。
• S080 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S079 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term10，不以小數近似替代。
• S078 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample10 value times cell width，不以小數近似替代。
• S077 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample10 affine value plus c，不以小數近似替代。
• S076 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample10 slope times x，不以小數近似替代。
• S075 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample10 lower plus offset，不以小數近似替代。
• S074 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample10 index times width，不以小數近似替代。
• S073 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S072 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term9，不以小數近似替代。
• S071 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample9 value times cell width，不以小數近似替代。
• S070 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample9 affine value plus c，不以小數近似替代。
• S069 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample9 slope times x，不以小數近似替代。
• S068 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample9 lower plus offset，不以小數近似替代。
• S067 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample9 index times width，不以小數近似替代。
• S066 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S065 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term8，不以小數近似替代。
• S064 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample8 value times cell width，不以小數近似替代。
• S063 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample8 affine value plus c，不以小數近似替代。
• S062 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample8 slope times x，不以小數近似替代。
• S061 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample8 lower plus offset，不以小數近似替代。
• S060 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample8 index times width，不以小數近似替代。
• S059 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S058 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term7，不以小數近似替代。
• S057 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample7 value times cell width，不以小數近似替代。
• S056 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample7 affine value plus c，不以小數近似替代。
• S055 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample7 slope times x，不以小數近似替代。
• S054 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample7 lower plus offset，不以小數近似替代。
• S053 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample7 index times width，不以小數近似替代。
• S052 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S051 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term6，不以小數近似替代。
• S050 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample6 value times cell width，不以小數近似替代。
• S049 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample6 affine value plus c，不以小數近似替代。
• S048 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample6 slope times x，不以小數近似替代。
• S047 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample6 lower plus offset，不以小數近似替代。
• S046 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample6 index times width，不以小數近似替代。
• S045 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S044 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term5，不以小數近似替代。
• S043 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample5 value times cell width，不以小數近似替代。
• S042 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample5 affine value plus c，不以小數近似替代。
• S041 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample5 slope times x，不以小數近似替代。
• S040 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample5 lower plus offset，不以小數近似替代。
• S039 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample5 index times width，不以小數近似替代。
• S038 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S037 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term4，不以小數近似替代。
• S036 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample4 value times cell width，不以小數近似替代。
• S035 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample4 affine value plus c，不以小數近似替代。
• S034 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample4 slope times x，不以小數近似替代。
• S033 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample4 lower plus offset，不以小數近似替代。
• S032 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample4 index times width，不以小數近似替代。
• S031 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S030 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term3，不以小數近似替代。
• S029 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample3 value times cell width，不以小數近似替代。
• S028 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample3 affine value plus c，不以小數近似替代。
• S027 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample3 slope times x，不以小數近似替代。
• S026 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample3 lower plus offset，不以小數近似替代。
• S025 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample3 index times width，不以小數近似替代。
• S024 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S023 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term2，不以小數近似替代。
• S022 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample2 value times cell width，不以小數近似替代。
• S021 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample2 affine value plus c，不以小數近似替代。
• S020 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample2 slope times x，不以小數近似替代。
• S019 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample2 lower plus offset，不以小數近似替代。
• S018 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample2 index times width，不以小數近似替代。
• S017 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S016 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term1，不以小數近似替代。
• S015 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample1 value times cell width，不以小數近似替代。
• S014 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample1 affine value plus c，不以小數近似替代。
• S013 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample1 slope times x，不以小數近似替代。
• S012 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample1 lower plus offset，不以小數近似替代。
• S011 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample1 index times width，不以小數近似替代。
• S010 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。
• S009 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL accumulated term0，不以小數近似替代。
• S008 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample0 value times cell width，不以小數近似替代。
• S007 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample0 affine value plus c，不以小數近似替代。
• S006 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample0 slope times x，不以小數近似替代。
• S005 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample0 lower plus offset，不以小數近似替代。
• S004 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL sample0 index times width，不以小數近似替代。
• S003 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL width over positive cell count，不以小數近似替代。
• S002 · premise_and_result_audit — 以精確有理數重算 Left sum ORIGINAL upper minus lower endpoint，不以小數近似替代。
• S001 · premise_and_result_audit — 以原始資料、欄位角色、型別、論域及本步前提反向代回核對；不表示結論能唯一還原前提。來源綁定候選、獨立審查、形式證明與發布分開。

結論

-605/2

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。