Question

求和：1/2+3/4+5/8+····+2n-1/2的n次方.

Answer 1

设k=1/2+3/4+5/8+……+(2n-1)/2^n

则 2k=1+3/2+5/4+……+(2n-1)/2^(n-1)

k=1+1+1/2+1/4+……+1/2^(n-2)-(2n-1)/2^n=3-1/2^(n-2)-(2n-1)/2^n=3-(2n+3)/2^n