lim(1+2+4+...+2^n-1)/(1+3

lim(1+2+4+...+2^n-1)/(1+3+9+...+3^n-1)

2个回答

等比数列
1+2+4+.+2^(n-1)=2^n-1
1+3+9+.+3^(n-1)=(3^n-1)/2
lim(1+2+4+...+2^n-1)/(1+3+9+...+3^n-1)=lim(2^n-1)/[(3^n-1)/2]=0

lim(n→无限大）An=1+1/3lim(n→无限大）*(1+4/9+(4/9)^2...+(4/9)^(n-2))
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