求下列极限lim(n
求下列极限lim(n->∞)(1-1/2)*(1-1/4)……(1-1/2^n)求下列极限lim(n->∞)(1-1/2)*(1-1/4)……(1-1/2^n)
u(n) = 1 1/2 1/4 ... 1/2^n = (1-1/2^(n 1) ) /(1-1/2) = 2 - 1/2^n
n->∞, 1/2^n ->0
lim(n->∞) u(n) = 2
答:lim (1+1/2+1/4+.....+1/2^n) ()里的就是等比数列求和 =lim[1-(1/2)^(n+1)]/(1-1/2) =2 lim{[(2x...详情>>
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