作者steve1012 (steve)
看板NTUBIME103HW
标题Re: [微甲] 12.2 36题不会
时间Sun Apr 17 19:50:04 2011
※ 引述《ZaX10A (Q﹏Q)》之铭言：
: 我看了答案还是阵亡...
: 救命呀!!!
利用提示 Sn = 1+2x +3x^2 ..... + (n-1) x^(n-2) + nx^(n-1)
-2xSn = -2x-4x^2 ..... - 2(n-2)x^(n-2) - 2(n-1)x^(n-1) -2nx^n
+ x^2Sn = +2x^2 ..... + (n-3) x^(n-2) + (n-2)x^(n-1)+(n-1)x^n+nx^n+1
+)__________________________________________________________________________
(1-x)^2* Sn = 1+0+0......-(1+n)x^n +nx^n+1
1- (1+n)x^n +nx^n+1
=> Sn= -----------------------
(1-x)^2
(这边其实不能用n因为n是离散的 要用变数比较严谨）
1- (1+n)x^n +nx^n+1 1
lim ------------------------ = ---------
n->infinity (1-x)^2 (1-x)^2 Q.E.D
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1F：推 ZaX10A:ㄙㄨ ㄍㄟˊ!!!!!!!!!!!! 3QQQ 04/17 23:37