Re: [分析] 高微(11)
※ 引述《PttFund (批踢踢基金只進不出)》之銘言：
: ※ 引述《PttFund (批踢踢基金只進不出)》之銘言：
: : ∞ (-1)^n
: : 請證明 Σ ------------ 收斂, 但不是絕對收斂.
: : n=2 n + (-1)^n
: (-1)^n 1 1
: Let a_n = ------------, then |a_n| = ------------ ≧ -----
: n + (-1)^n n + (-1)^n n+1
: for n≧2. Note that |a_n|≧1/(n+1)≧0 for n≧2 and Σ1/(n+1)
: diverges. Hence Σ|a_n| also diverges, that is, Σa_n does
: not converge absolutely.
: 因此不是絕對收斂. 至於收斂, 這還要想一下喔 ＠ｏ＠
Hence (a_2+a_3)+..... 遞減至 -(1/2*3+1/4*5+.....)
又 a_n -->0, so the series converges,
indeed, the sum=log2-1
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 220.135.132.108
→
140.115.205.107 07/25, , 1F
140.115.205.107 07/25, 1F
→
140.115.205.107 07/25, , 2F
140.115.205.107 07/25, 2F
推
61.219.178.197 07/25, , 3F
61.219.178.197 07/25, 3F
推
61.219.178.197 07/25, , 4F
61.219.178.197 07/25, 4F
推
220.135.132.108 07/25, , 5F
220.135.132.108 07/25, 5F
推
140.115.205.107 07/25, , 6F
140.115.205.107 07/25, 6F
討論串 (同標題文章)