1/2+1/4+1/8+...1/2的n次方
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1/2+1/4+1/8+...1/2的n次方
=2×(1/2+1/4+1/8+...1/2的n次方) -(1/2+1/4+1/8+...1/2的n次方)
=1+1/2+1/4+1/8+...1/2的n-1次方- (1/2+1/4+1/8+...+1/2的n-次方+1/2的n次方)
=1+(1/2- 1/2)+(1/4-1/4)+(1/8-1/8)+...(1/2的n-1次方-1/2的n-1次方)-1/2的n次方
=1- 1/2的n次方
=2×(1/2+1/4+1/8+...1/2的n次方) -(1/2+1/4+1/8+...1/2的n次方)
=1+1/2+1/4+1/8+...1/2的n-1次方- (1/2+1/4+1/8+...+1/2的n-次方+1/2的n次方)
=1+(1/2- 1/2)+(1/4-1/4)+(1/8-1/8)+...(1/2的n-1次方-1/2的n-1次方)-1/2的n次方
=1- 1/2的n次方
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