Sn=2/2+3/2²+4/2³+····+(n+1)/(2^n) 求Sn.

问题描述:

Sn=2/2+3/2²+4/2³+····+(n+1)/(2^n) 求Sn.

Sn=2/2+3/2²+4/2³+····…+n/2^(n-1)+(n+1)/(2^n) 2Sn=2+3/2+4/2²+5/2³+……+(n+1)/2^(n-1)下减上得Sn=2+[(1/2)+(1/4)+(1/8)+……+[1/2^(n-1)]]-(n+1)/2^n=2+{1/2[1-(1/2)^(n-1)]/(1-1/2)}-(...