求和Sn=1+(1+1/2)+(1+1/2+1/4)+.+[1+1/2+1/4.+1/2^(n-1)]

Question

求和Sn=1+(1+1/2)+(1+1/2+1/4)+.+[1+1/2+1/4.+1/2^(n-1)]

Answer 1

Sn=(2-1)+(2-1/2)+(2-1/4)+.{2-1/2^(n-1)}
=2*n-[1+1/2+1/4+.1/2^(n-1)]
=2n-{2-1/2^(n-1)]
=2n-2+1/2^(n-1)
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