# 單調有界數列收斂定理基礎 · 脈衝 R02

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-foundations · 2026-10-14 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[1,2],"coefficient":1,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 1/2, 1, 2, [0, 1/6, 1/4], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 1/2, 1, 2, [0, 1/6, 1/4], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0001/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 2. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[2,3],"coefficient":2,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 2/3, 2, 2, [-1/3, 0, 1/6], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 2/3, 2, 2, [-1/3, 0, 1/6], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0002/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 3. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[3,4],"coefficient":3,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 3/4, 3, 2, [-3/4, -1/4, 0], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 3/4, 3, 2, [-3/4, -1/4, 0], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0003/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 4. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[4,5],"coefficient":4,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 4/5, 4, 2, [-6/5, -8/15, -1/5], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 4/5, 4, 2, [-6/5, -8/15, -1/5], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0004/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 5. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[5,6],"coefficient":5,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 5/6, 5, 2, [-5/3, -5/6, -5/12], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 5/6, 5, 2, [-5/3, -5/6, -5/12], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0005/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 6. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[6,7],"coefficient":6,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 6/7, 6, 2, [-15/7, -8/7, -9/14], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 6/7, 6, 2, [-15/7, -8/7, -9/14], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0006/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 7. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[7,8],"coefficient":7,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 7/8, 7, 2, [-21/8, -35/24, -7/8], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 7/8, 7, 2, [-21/8, -35/24, -7/8], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0007/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 8. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[8,9],"coefficient":8,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 8/9, 8, 2, [-28/9, -16/9, -10/9], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 8/9, 8, 2, [-28/9, -16/9, -10/9], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0008/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 9. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[9,10],"coefficient":9,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 9/10, 9, 2, [-18/5, -21/10, -27/20], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 9/10, 9, 2, [-18/5, -21/10, -27/20], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0009/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 10. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[10,11],"coefficient":10,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 10/11, 10, 2, [-45/11, -80/33, -35/22], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 10/11, 10, 2, [-45/11, -80/33, -35/22], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0010/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 11. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[11,12],"coefficient":11,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 11/12, 11, 2, [-55/12, -11/4, -11/6], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 11/12, 11, 2, [-55/12, -11/4, -11/6], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0011/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 12. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[12,13],"coefficient":12,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 12/13, 12, 2, [-66/13, -40/13, -27/13], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 12/13, 12, 2, [-66/13, -40/13, -27/13], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0012/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 13. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[13,14],"coefficient":13,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 13/14, 13, 2, [-39/7, -143/42, -65/28], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 13/14, 13, 2, [-39/7, -143/42, -65/28], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0013/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 14. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[14,15],"coefficient":14,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 14/15, 14, 2, [-91/15, -56/15, -77/30], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 14/15, 14, 2, [-91/15, -56/15, -77/30], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0014/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 15. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[15,16],"coefficient":15,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 15/16, 15, 2, [-105/16, -65/16, -45/16], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 15/16, 15, 2, [-105/16, -65/16, -45/16], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0015/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 16. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[16,17],"coefficient":16,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 16/17, 16, 2, [-120/17, -224/51, -52/17], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 16/17, 16, 2, [-120/17, -224/51, -52/17], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0016/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 17. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[17,18],"coefficient":17,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 17/18, 17, 2, [-68/9, -85/18, -119/36], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 17/18, 17, 2, [-68/9, -85/18, -119/36], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0017/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 18. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[18,19],"coefficient":18,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 18/19, 18, 2, [-153/19, -96/19, -135/38], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 18/19, 18, 2, [-153/19, -96/19, -135/38], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0018/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 19. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[19,20],"coefficient":19,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 19/20, 19, 2, [-171/20, -323/60, -19/5], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 19/20, 19, 2, [-171/20, -323/60, -19/5], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0019/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 20. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[20,21],"coefficient":20,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 20/21, 20, 2, [-190/21, -40/7, -85/21], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 20/21, 20, 2, [-190/21, -40/7, -85/21], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0020/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 21. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[21,22],"coefficient":21,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 21/22, 21, 2, [-105/11, -133/22, -189/44], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 21/22, 21, 2, [-105/11, -133/22, -189/44], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0021/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 22. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[22,23],"coefficient":22,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 22/23, 22, 2, [-231/23, -440/69, -209/46], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 22/23, 22, 2, [-231/23, -440/69, -209/46], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0022/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 23. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[23,24],"coefficient":23,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 23/24, 23, 2, [-253/24, -161/24, -115/24], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 23/24, 23, 2, [-253/24, -161/24, -115/24], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0023/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 24. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[24,25],"coefficient":24,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 24/25, 24, 2, [-276/25, -176/25, -126/25], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 24/25, 24, 2, [-276/25, -176/25, -126/25], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0024/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 25. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-increasing-limit-certificate；資料={"limit":[25,26],"coefficient":25,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 25/26, 25, 2, [-150/13, -575/78, -275/52], 是, nondecreasing_bounded_above_supremum_limit)

Wave6第二層核對=(increasing, 25/26, 25, 2, [-150/13, -575/78, -275/52], 是, nondecreasing_bounded_above_supremum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0025/)

單調有界數列收斂定理 · qf-mod39-monoseq-increasing-limit-certificate · candidate





## 26. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[1,2],"coefficient":1,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 1/2, 1, 2, [1, 5/6, 3/4], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 1/2, 1, 2, [1, 5/6, 3/4], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0026/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 27. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[2,3],"coefficient":2,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 2/3, 2, 2, [5/3, 4/3, 7/6], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 2/3, 2, 2, [5/3, 4/3, 7/6], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0027/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 28. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[3,4],"coefficient":3,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 3/4, 3, 2, [9/4, 7/4, 3/2], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 3/4, 3, 2, [9/4, 7/4, 3/2], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0028/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 29. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[4,5],"coefficient":4,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 4/5, 4, 2, [14/5, 32/15, 9/5], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 4/5, 4, 2, [14/5, 32/15, 9/5], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0029/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 30. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[5,6],"coefficient":5,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 5/6, 5, 2, [10/3, 5/2, 25/12], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 5/6, 5, 2, [10/3, 5/2, 25/12], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0030/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 31. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[6,7],"coefficient":6,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 6/7, 6, 2, [27/7, 20/7, 33/14], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 6/7, 6, 2, [27/7, 20/7, 33/14], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0031/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 32. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[7,8],"coefficient":7,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 7/8, 7, 2, [35/8, 77/24, 21/8], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 7/8, 7, 2, [35/8, 77/24, 21/8], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0032/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 33. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[8,9],"coefficient":8,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 8/9, 8, 2, [44/9, 32/9, 26/9], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 8/9, 8, 2, [44/9, 32/9, 26/9], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0033/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 34. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[9,10],"coefficient":9,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 9/10, 9, 2, [27/5, 39/10, 63/20], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 9/10, 9, 2, [27/5, 39/10, 63/20], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0034/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 35. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[10,11],"coefficient":10,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 10/11, 10, 2, [65/11, 140/33, 75/22], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 10/11, 10, 2, [65/11, 140/33, 75/22], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0035/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 36. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[11,12],"coefficient":11,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 11/12, 11, 2, [77/12, 55/12, 11/3], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 11/12, 11, 2, [77/12, 55/12, 11/3], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0036/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 37. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[12,13],"coefficient":12,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 12/13, 12, 2, [90/13, 64/13, 51/13], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 12/13, 12, 2, [90/13, 64/13, 51/13], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0037/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 38. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[13,14],"coefficient":13,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 13/14, 13, 2, [52/7, 221/42, 117/28], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 13/14, 13, 2, [52/7, 221/42, 117/28], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0038/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 39. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[14,15],"coefficient":14,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 14/15, 14, 2, [119/15, 28/5, 133/30], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 14/15, 14, 2, [119/15, 28/5, 133/30], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0039/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 40. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[15,16],"coefficient":15,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 15/16, 15, 2, [135/16, 95/16, 75/16], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 15/16, 15, 2, [135/16, 95/16, 75/16], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0040/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 41. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[16,17],"coefficient":16,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 16/17, 16, 2, [152/17, 320/51, 84/17], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 16/17, 16, 2, [152/17, 320/51, 84/17], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0041/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 42. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[17,18],"coefficient":17,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 17/18, 17, 2, [85/9, 119/18, 187/36], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 17/18, 17, 2, [85/9, 119/18, 187/36], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0042/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 43. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[18,19],"coefficient":18,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 18/19, 18, 2, [189/19, 132/19, 207/38], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 18/19, 18, 2, [189/19, 132/19, 207/38], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0043/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 44. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[19,20],"coefficient":19,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 19/20, 19, 2, [209/20, 437/60, 57/10], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 19/20, 19, 2, [209/20, 437/60, 57/10], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0044/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 45. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[20,21],"coefficient":20,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 20/21, 20, 2, [230/21, 160/21, 125/21], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 20/21, 20, 2, [230/21, 160/21, 125/21], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0045/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 46. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[21,22],"coefficient":21,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 21/22, 21, 2, [126/11, 175/22, 273/44], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 21/22, 21, 2, [126/11, 175/22, 273/44], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0046/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 47. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[22,23],"coefficient":22,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 22/23, 22, 2, [275/23, 572/69, 297/46], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 22/23, 22, 2, [275/23, 572/69, 297/46], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0047/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 48. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[23,24],"coefficient":23,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 23/24, 23, 2, [299/24, 69/8, 161/24], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 23/24, 23, 2, [299/24, 69/8, 161/24], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0048/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 49. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[24,25],"coefficient":24,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 24/25, 24, 2, [324/25, 224/25, 174/25], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 24/25, 24, 2, [324/25, 224/25, 174/25], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0049/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 50. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-decreasing-limit-certificate；資料={"limit":[25,26],"coefficient":25,"shift":2}。請依 [direction, limit, coefficient, shift, first_three_terms, symbolic_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 25/26, 25, 2, [175/13, 725/78, 375/52], 是, nonincreasing_bounded_below_infimum_limit)

Wave6第二層核對=(decreasing, 25/26, 25, 2, [175/13, 725/78, 375/52], 是, nonincreasing_bounded_below_infimum_limit)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0050/)

單調有界數列收斂定理 · qf-mod39-monoseq-decreasing-limit-certificate · candidate





## 51. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[1,2],"coefficient":1,"shift":2,"epsilon":[1,10]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 1/2, 1/10, 9, 9/22, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 1/2, 1/10, 9, 9/22, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0051/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 52. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"decreasing","limit":[2,3],"coefficient":2,"shift":2,"epsilon":[1,11]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 2/3, 1/11, 21, 52/69, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(decreasing, 2/3, 1/11, 21, 52/69, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0052/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 53. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[3,4],"coefficient":3,"shift":2,"epsilon":[1,12]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 3/4, 1/12, 35, 99/148, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 3/4, 1/12, 35, 99/148, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0053/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 54. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"decreasing","limit":[4,5],"coefficient":4,"shift":2,"epsilon":[1,13]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 4/5, 1/13, 51, 232/265, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(decreasing, 4/5, 1/13, 51, 232/265, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0054/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 55. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[5,6],"coefficient":5,"shift":2,"epsilon":[1,14]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 5/6, 1/14, 69, 325/426, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 5/6, 1/14, 69, 325/426, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0055/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 56. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"decreasing","limit":[6,7],"coefficient":6,"shift":2,"epsilon":[1,15]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 6/7, 1/15, 89, 12/13, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(decreasing, 6/7, 1/15, 89, 12/13, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0056/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 57. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[7,8],"coefficient":7,"shift":2,"epsilon":[1,16]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 7/8, 1/16, 111, 735/904, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 7/8, 1/16, 111, 735/904, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0057/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 58. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"decreasing","limit":[8,9],"coefficient":8,"shift":2,"epsilon":[1,17]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 8/9, 1/17, 135, 1168/1233, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(decreasing, 8/9, 1/17, 135, 1168/1233, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0058/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 59. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[9,10],"coefficient":9,"shift":2,"epsilon":[1,18]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 9/10, 1/18, 161, 1377/1630, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 9/10, 1/18, 161, 1377/1630, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0059/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 60. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"decreasing","limit":[10,11],"coefficient":10,"shift":2,"epsilon":[1,19]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 10/11, 1/19, 189, 2020/2101, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(decreasing, 10/11, 1/19, 189, 2020/2101, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0060/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 61. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[11,12],"coefficient":11,"shift":2,"epsilon":[1,20]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 11/12, 1/20, 219, 2299/2652, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 11/12, 1/20, 219, 2299/2652, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0061/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 62. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"decreasing","limit":[12,13],"coefficient":12,"shift":2,"epsilon":[1,21]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 12/13, 1/21, 251, 3192/3289, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(decreasing, 12/13, 1/21, 251, 3192/3289, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0062/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 63. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[13,14],"coefficient":13,"shift":2,"epsilon":[1,22]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 13/14, 1/22, 285, 507/574, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 13/14, 1/22, 285, 507/574, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0063/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 64. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"decreasing","limit":[14,15],"coefficient":14,"shift":2,"epsilon":[1,23]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 14/15, 1/23, 321, 4732/4845, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(decreasing, 14/15, 1/23, 321, 4732/4845, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0064/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 65. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[15,16],"coefficient":15,"shift":2,"epsilon":[1,24]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 15/16, 1/24, 359, 5175/5776, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 15/16, 1/24, 359, 5175/5776, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0065/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 66. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"decreasing","limit":[16,17],"coefficient":16,"shift":2,"epsilon":[1,25]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 16/17, 1/25, 399, 6688/6817, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(decreasing, 16/17, 1/25, 399, 6688/6817, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0066/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 67. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[17,18],"coefficient":17,"shift":2,"epsilon":[1,26]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 17/18, 1/26, 441, 7225/7974, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 17/18, 1/26, 441, 7225/7974, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0067/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 68. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"decreasing","limit":[18,19],"coefficient":18,"shift":2,"epsilon":[1,27]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 18/19, 1/27, 485, 9108/9253, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(decreasing, 18/19, 1/27, 485, 9108/9253, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0068/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 69. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[19,20],"coefficient":19,"shift":2,"epsilon":[1,28]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 19/20, 1/28, 531, 9747/10660, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 19/20, 1/28, 531, 9747/10660, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0069/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 70. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"decreasing","limit":[20,21],"coefficient":20,"shift":2,"epsilon":[1,29]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 20/21, 1/29, 579, 1720/1743, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(decreasing, 20/21, 1/29, 579, 1720/1743, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0070/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 71. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[21,22],"coefficient":21,"shift":2,"epsilon":[1,30]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 21/22, 1/30, 629, 12789/13882, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 21/22, 1/30, 629, 12789/13882, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0071/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 72. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"decreasing","limit":[22,23],"coefficient":22,"shift":2,"epsilon":[1,31]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 22/23, 1/31, 681, 15532/15709, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(decreasing, 22/23, 1/31, 681, 15532/15709, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0072/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 73. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[23,24],"coefficient":23,"shift":2,"epsilon":[1,32]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 23/24, 1/32, 735, 16399/17688, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 23/24, 1/32, 735, 16399/17688, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0073/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 74. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"decreasing","limit":[24,25],"coefficient":24,"shift":2,"epsilon":[1,33]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(decreasing, 24/25, 1/33, 791, 19632/19825, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(decreasing, 24/25, 1/33, 791, 19632/19825, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0074/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 75. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-epsilon-witness；資料={"direction":"increasing","limit":[25,26],"coefficient":25,"shift":2,"epsilon":[1,34]}。請依 [direction, limit, epsilon, N, value_at_N, strict_tail_certificate, certificate] 欄序回答。

查看答案與解釋(increasing, 25/26, 1/34, 849, 20625/22126, 是, forall_n_ge_N_by_monotone_symbolic_tail)

Wave6第二層核對=(increasing, 25/26, 1/34, 849, 20625/22126, 是, forall_n_ge_N_by_monotone_symbolic_tail)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0075/)

單調有界數列收斂定理 · qf-mod39-monoseq-epsilon-witness · candidate





## 76. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"monotone_unbounded","prefix_length":3}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(monotone_unbounded, [0, 1, 2], 是, 否, 否, monotone_without_bound_not_covered)

Wave6第二層核對=(monotone_unbounded, [0, 1, 2], 是, 否, 否, monotone_without_bound_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0076/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 77. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"bounded_nonmonotone","prefix_length":4}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(bounded_nonmonotone, [1, -1, 1, -1], 否, 是, 否, bounded_without_monotonicity_not_covered)

Wave6第二層核對=(bounded_nonmonotone, [1, -1, 1, -1], 否, 是, 否, bounded_without_monotonicity_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0077/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 78. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"finite_prefix_only","prefix_length":5}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(finite_prefix_only, 5, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)

Wave6第二層核對=(finite_prefix_only, 5, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0078/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 79. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"monotone_unbounded","prefix_length":6}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(monotone_unbounded, [0, 1, 2, 3, 4, 5], 是, 否, 否, monotone_without_bound_not_covered)

Wave6第二層核對=(monotone_unbounded, [0, 1, 2, 3, 4, 5], 是, 否, 否, monotone_without_bound_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0079/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 80. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"bounded_nonmonotone","prefix_length":7}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1], 否, 是, 否, bounded_without_monotonicity_not_covered)

Wave6第二層核對=(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1], 否, 是, 否, bounded_without_monotonicity_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0080/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 81. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"finite_prefix_only","prefix_length":8}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(finite_prefix_only, 8, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)

Wave6第二層核對=(finite_prefix_only, 8, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0081/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 82. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"monotone_unbounded","prefix_length":9}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8], 是, 否, 否, monotone_without_bound_not_covered)

Wave6第二層核對=(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8], 是, 否, 否, monotone_without_bound_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0082/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 83. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"bounded_nonmonotone","prefix_length":10}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1], 否, 是, 否, bounded_without_monotonicity_not_covered)

Wave6第二層核對=(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1], 否, 是, 否, bounded_without_monotonicity_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0083/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 84. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"finite_prefix_only","prefix_length":11}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(finite_prefix_only, 11, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)

Wave6第二層核對=(finite_prefix_only, 11, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0084/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 85. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"monotone_unbounded","prefix_length":12}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是, 否, 否, monotone_without_bound_not_covered)

Wave6第二層核對=(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是, 否, 否, monotone_without_bound_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0085/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 86. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"bounded_nonmonotone","prefix_length":13}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 否, 是, 否, bounded_without_monotonicity_not_covered)

Wave6第二層核對=(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 否, 是, 否, bounded_without_monotonicity_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0086/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 87. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"finite_prefix_only","prefix_length":14}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(finite_prefix_only, 14, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)

Wave6第二層核對=(finite_prefix_only, 14, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0087/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 88. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"monotone_unbounded","prefix_length":15}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], 是, 否, 否, monotone_without_bound_not_covered)

Wave6第二層核對=(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], 是, 否, 否, monotone_without_bound_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0088/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 89. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"bounded_nonmonotone","prefix_length":16}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], 否, 是, 否, bounded_without_monotonicity_not_covered)

Wave6第二層核對=(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], 否, 是, 否, bounded_without_monotonicity_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0089/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 90. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"finite_prefix_only","prefix_length":17}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(finite_prefix_only, 17, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)

Wave6第二層核對=(finite_prefix_only, 17, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0090/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 91. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"monotone_unbounded","prefix_length":18}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 是, 否, 否, monotone_without_bound_not_covered)

Wave6第二層核對=(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 是, 否, 否, monotone_without_bound_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0091/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 92. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"bounded_nonmonotone","prefix_length":19}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 否, 是, 否, bounded_without_monotonicity_not_covered)

Wave6第二層核對=(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 否, 是, 否, bounded_without_monotonicity_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0092/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 93. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"finite_prefix_only","prefix_length":20}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(finite_prefix_only, 20, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)

Wave6第二層核對=(finite_prefix_only, 20, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0093/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 94. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"monotone_unbounded","prefix_length":21}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], 是, 否, 否, monotone_without_bound_not_covered)

Wave6第二層核對=(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], 是, 否, 否, monotone_without_bound_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0094/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 95. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"bounded_nonmonotone","prefix_length":22}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], 否, 是, 否, bounded_without_monotonicity_not_covered)

Wave6第二層核對=(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], 否, 是, 否, bounded_without_monotonicity_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0095/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 96. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"finite_prefix_only","prefix_length":23}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(finite_prefix_only, 23, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)

Wave6第二層核對=(finite_prefix_only, 23, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0096/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 97. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"monotone_unbounded","prefix_length":24}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 是, 否, 否, monotone_without_bound_not_covered)

Wave6第二層核對=(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 是, 否, 否, monotone_without_bound_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0097/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 98. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"bounded_nonmonotone","prefix_length":25}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 否, 是, 否, bounded_without_monotonicity_not_covered)

Wave6第二層核對=(bounded_nonmonotone, [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 否, 是, 否, bounded_without_monotonicity_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0098/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 99. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"finite_prefix_only","prefix_length":26}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(finite_prefix_only, 26, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)

Wave6第二層核對=(finite_prefix_only, 26, 否, 否, 否, finite_prefix_not_universal_monotone_bounded_certificate)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0099/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate





## 100. 單調有界數列收斂定理

實數列的symbolic全稱單調與相應有界證書。操作=monoseq-hypothesis-boundary；資料={"mode":"monotone_unbounded","prefix_length":27}。請依 [mode, prefix_or_length, monotone_premise_certified, relevant_bound_certified, theorem_applicability_certified, boundary] 欄序回答。

finite_prefix_only的否表示沒有全稱前提證書，不是否定未知延伸的單調、有界或收斂性；另兩模式使用明示的完整反例族。

查看答案與解釋(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], 是, 否, 否, monotone_without_bound_not_covered)

Wave6第二層核對=(monotone_unbounded, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], 是, 否, 否, monotone_without_bound_not_covered)；依完整明示資料獨立重算；nondecreasing加上界時極限為sup，nonincreasing加下界時為inf；sup不必是maximum；epsilon證明以s-epsilon不是上界取得index再由monotonicity控制tail；finite prefix不足且convergence不推monotone。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-0100/)

單調有界數列收斂定理 · qf-mod39-monoseq-hypothesis-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261108-r02-monotone-sequence-convergence-theorem-foundations/validation-report.json)