求极限:lim(n→∞) (1+2+4+8+...+2^n)/2^n
人气:457 ℃ 时间:2020-02-05 04:59:02
解答
利用等比数列求和公式1+2+4+...+2^n=2^0+2^1+...+2^n=2^0(1-2^(n+1))/(1-2)=2^(n+1) -1
lim(n→∞) (1+2+4+8+...+2^n)/2^n
= lim(n→∞)((2^(n+1) -1)/2^n)
= lim(n→∞)(2- 1/2^n)
=2-0
=2
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