Sn=1*2+3*2^2+5*2^3+……+(2n-1)*2^n 求Sn=
问题描述:
Sn=1*2+3*2^2+5*2^3+……+(2n-1)*2^n 求Sn=
答
Sn=1*2+3*2^2+5*2^3+……+(2n-1)*2^n2Sn=1*2^2+3*2^3+...+(2n-1)*2^(n+1)相减得-Sn=1*2+2*2^2+2*2^3+..+2*2^n-(2n-1)*2^(n+1)=1*2+[2*2^2+2*2^3+..+2*2^n]-(2n-1)*2^(n+1)之后[]里的用等比数列求和公式算化简得sn=2 ...