求和：n-n/2^n

S1 = 1/2^1 + 2/2^2 + 3/2^3 + …… + n/2^n2S1 =1/2^0 + 2/2^1 + 3/2^2 + …… + n/2^(n-1)S1 = 2S1 - S1=1/2^0 + (2/2^1 -1/2^1 ) + (3/2^2 - 2/2^2 )+ …… + [ n/2^(n-1) - (n-1)/2^(n-1) ] - n/2^n= 1/2^0 + 1/2^1 + 1/2^2 + …… + 1/2^(n-1) - n/2^n= ( 1 - 1/2^n )/( 1 - 1/2 )- n/2^n= 2 - 2/2^n -n/2^n = 2 - ( 2 + n )/2^n；S = 1 + 2 + …… + n - (1/2^1 + 2/2^2 + 3/2^3 + …… + n/2^n )= n( n + 1 )/2 - S1=n( n + 1 )/2 -2 + ( 2 + n )/2^n 。