[微積] 級數 數列 收斂

看板Math作者 (Gloria)時間12年前 (2013/10/11 12:04), 編輯推噓4(4推 0噓 11→)
留言15則, 6人參與, 6年前最新討論串1/1
assume a_k -> 0 and | sum_{n=k}^{infinity} a_n | < M show that sum_{n=k}^{infinity} a_n -> 0 T or F 這有名字嗎 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 99.10.121.36
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10/11 12:25, , 1F
F,令a_n = 1/nn
10/11 12:25, 1F
推
10/11 12:35, , 2F
10/11 12:35, 2F
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10/11 12:53, , 3F
thx, how about adding |a_k|>0 ?
10/11 12:53, 3F
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10/11 12:54, , 4F
what is 1/nn? 1/(n*n)?
10/11 12:54, 4F
推
10/11 13:22, , 5F
題目好怪 既然寫 |Σk..∞ a_n| < M,
10/11 13:22, 5F
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10/11 13:22, , 6F
不就代表必須承認 |Σa_k| 的收斂了嗎?
10/11 13:22, 6F
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10/11 13:29, , 7F
還是題目其實只 abs. of partial sum 都一致有界?
10/11 13:29, 7F
推
10/11 13:34, , 8F
Yes it works.
10/11 13:34, 8F
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10/11 13:35, , 9F
隨便寫一串符號，不代表其中有任何意義。
10/11 13:35, 9F
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10/11 14:07, , 10F
so how to prove it or where to find reference
10/11 14:07, 10F
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10/11 14:33, , 11F
10/11 14:33, 11F
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10/11 15:08, , 12F
why can you conclude that S_k->0 directly?
10/11 15:08, 12F
推
10/11 22:00, , 13F
updated
10/11 22:00, 13F
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01/02 15:33, 7年前 , 14F
thx, how ab https://noxiv.com
01/02 15:33, 14F
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07/07 11:31, 6年前 , 15F
隨便寫一串符號，不代表 https://moxox.com
07/07 11:31, 15F
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