Re: [分析] 一題求極限值
※ 引述《kyoiku (生死間有大恐怖)》之銘言：
: 設 a_n -> 5 as n -> oo
: b_n -> 3 as n -> oo
: Sigma(k from 1 to n-1) k(a_k)(b_(n-k))
: 求 lim ----------------------------------------
: n->oo n^2
: 就是 (a_1)(b_n-1) + 2(a_2)(b_n-2) + ... + (n-1)(a_n-1)(b_1)
: ------------------------------------------------------
: n^2
: 趨近於多少當 n 趨近於無窮大
對於任意給定小數ε << 1
必然可找到n > M, |a_nb_n - 15| < ε/ 3
a_1b_(n-1) + ... + Na_nb_(n-M) M(M + 1)15
必可找到n >= N, |-------------------------------- _ ------------| < ε/ 3
n^2 4 n^2
則當n >= max{N, M+1, 45/(2ε)}
(n + M)(n - M - 1)
|原式 - 15/2| ≦ ε / 3 + --------------------ε / 3 + ε / 3
2n^2
< ε
=> 極限值 = 15 / 2
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 220.136.208.79
※ 文章網址: https://www.ptt.cc/bbs/Math/M.1421692976.A.CC3.html
推
01/20 03:20, , 1F
01/20 03:20, 1F
→
01/20 03:23, , 2F
01/20 03:23, 2F
→
01/20 03:23, , 3F
01/20 03:23, 3F
→
01/20 03:25, , 4F
01/20 03:25, 4F
推
01/20 21:13, , 5F
01/20 21:13, 5F
→
01/24 08:48, , 6F
01/24 08:48, 6F
→
01/24 08:48, , 7F
01/24 08:48, 7F
討論串 (同標題文章)