lim(1+1/2)+(1+2^2)(1+2^4)…(1+1/2^(2^(n-1))) n→∞lim(1+1/2)(1+1/2^2)(1+1/2^4)…(1+1/2^(2^(n-1))) n→∞

来源：学生作业帮助网 编辑：作业帮 时间：2024/07/18 20:35:38
lim(1+1/2)+(1+2^2)(1+2^4)…(1+1/2^(2^(n-1))) n→∞lim(1+1/2)(1+1/2^2)(1+1/2^4)…(1+1/2^(2^(n-1))) n→∞
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lim(1+1/2)+(1+2^2)(1+2^4)…(1+1/2^(2^(n-1))) n→∞lim(1+1/2)(1+1/2^2)(1+1/2^4)…(1+1/2^(2^(n-1))) n→∞
lim(1+1/2)+(1+2^2)(1+2^4)…(1+1/2^(2^(n-1))) n→∞
lim(1+1/2)(1+1/2^2)(1+1/2^4)…(1+1/2^(2^(n-1))) n→∞

lim(1+1/2)+(1+2^2)(1+2^4)…(1+1/2^(2^(n-1))) n→∞lim(1+1/2)(1+1/2^2)(1+1/2^4)…(1+1/2^(2^(n-1))) n→∞
给极限乘以一个(1-1/2),最后再除以它,就可以了,
原式=2lim(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)…(1+1/2^(2^(n-1)))
=2lim[1-1/2^(2^n )] (n→∞)
=2

lim(1+1/2)+(1+2^2)(1+2^4)…(1+1/2^(2^(n-1))) n→∞
lim(1+1/2)(1+1/2^2)(1+1/2^4)…(1+1/2^(2^(n-1))) n→∞
给极限乘以一个(1-1/2)，最后再除以它，就可以了，
原式=2lim(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)…(1+1/2^(2^(n-1)))
=2lim[1-1/2^(2^n )] (n→∞)
=2

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