作者rygb (再生)
看板trans_math
标题Re: [歛散] 请教一题级数审歛
时间Thu Jun 23 11:23:19 2011
※ 引述《jjerry8888 (夏兰行德枫)》之铭言：
: ∞
: Σ n^2e^(-n^3)
: n=1
: 此题是要用哪一种方法判断歛散性啊?
n^2
------- = an an always > 0 and an+1 < an
(n^3)
e
Use Integral Test
1 1 3 1 -(n^3) |n=0 1
-- ∫ ------ d n = --- e | = ---- so its converge
3 n^3 3 |n=∞ 3
e
Use Limit Comparison Test
an
we know that if lim ---- = 0 and Σbn converge , then Σan converge
n->∞ bn
1
Σbn = Σ---
2
n
an
lim ----- = 0 and Σbn is p-series p >2 so Σbn converge
n->∞ bn
then Σan converge
--
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◆ From: 114.34.122.244
※ 编辑: rygb 来自: 114.34.122.244 (06/23 11:24)
1F：推 jjerry8888:感谢罗!!! 163.25.118.163 06/23 11:43