[微積] 級數 數列 收斂

[GSXSP (Gloria)]

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

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◆ From: 99.10.121.36
→ nonumber    :F,令a_n = 1/nn
推 redo        :http://calculus.dkd.tw/demo/?q=node/11
→ GSXSP       :thx, how about adding |a_k|>0 ?
→ GSXSP       :what is 1/nn?  1/(n*n)?
推 suhorng     :題目好怪 既然寫 |Σk..∞ a_n| < M,
→ suhorng     :不就代表必須承認 |Σa_k| 的收斂了嗎?
→ suhorng     :還是題目其實只 abs. of partial sum 都一致有界?
推 redo        :Yes it works.
→ redo        :隨便寫一串符號，不代表其中有任何意義。
→ GSXSP       :so how to prove it or where to find reference
→ redo        :http://calculus.dkd.tw/demo/?q=node/11
→ GSXSP       :why can you conclude that S_k->0 directly?
推 redo        :updated
→ sneak       : thx, how ab https://noxiv.com
→ muxiv       : 隨便寫一串符號，不代表 https://moxox.com