等比数列求和 1+(1+1/2)+(1+1/2+1/4)+.+((1+1/2+1/4+.+1/2^(n-1))麻烦写下具体过程

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等比数列求和 1+(1+1/2)+(1+1/2+1/4)+.+((1+1/2+1/4+.+1/2^(n-1))麻烦写下具体过程
等比数列求和 1+(1+1/2)+(1+1/2+1/4)+.+((1+1/2+1/4+.+1/2^(n-1))麻烦写下具体过程

等比数列求和 1+(1+1/2)+(1+1/2+1/4)+.+((1+1/2+1/4+.+1/2^(n-1))麻烦写下具体过程
1+(1+1/2)+(1+1/2+1/4)+.+((1+1/2+1/4+.+1/2^(n-1))
=(1+1-1)+(1+1/2+1/2-1/2)+(1+1/2+1/4+1/4-1/4)+……((1+1/2+1/4+.+1/2^(n-1)+1/2^(n-1)-1/2^(n-1))
=(2-1)+(2-1/2)+(2-1/4)+(2-1/8)+……+(2-1/2^(n-1))
=2n-(1+1/2+……+1/2^(n-1)+1/2^(n-1)-1/2^(n-1))
=2n-2+1/2^(n-1)