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

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

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)}-(n+1)/2^n
=2+1-1/[2^(n-1)]-(n+1)/2^n
=3-2/2^n-(n+1)/2^n
=3-(2+n+1)/2^n
=3-[(3+n)/2^n]