1/2+1/2²+1/2³+1/3的4次方…+1/2n次方=多少

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1/2+1/2²+1/2³+1/3的4次方…+1/2n次方=多少
1/2+1/2²+1/2³+1/3的4次方…+1/2n次方=多少

1/2+1/2²+1/2³+1/3的4次方…+1/2n次方=多少
1-1/2n次方

S=1/2+1/2²+1/2³+1/2⁴…+1/2^n ①
2S=1+1/2+1/2²+1/2³+1/2⁴…+1/2^(n-1) ②
②-①得S=1-1/2^n=(2^n-1)/2^n
即1/2+1/2²+1/2³+1/2⁴…+1/2^n=(2^n-1)/2^n