帮我求一个极限limn->无穷[1/2+1/4+1/8+.+(1/2)^n]就是求数列{1/2^n}的极限

Question

帮我求一个极限
lim n->无穷 [1/2+1/4+1/8+.+(1/2)^n]
就是求数列{1/2^n}的极限

Answer 1

lim [1/2+1/4+1/8+.+(1/2)^n]
n→∞
=lim {1/2·[1 - (1/2)^(n-1)]} / [1 - (1/2)]
n→∞
=lim [1 - (1/2)^(n-1)]
n→∞
= 1
解题说明：数列{1/2^n}是一个等比数列,先代入前 n 项和公式,即可得出极限结果.