Sn=2*2^1+3*2^2+4*2^3+…………+（n+1）*2^n
2Sn=2*2^2+3*2^3+4*2^4+…………(n+1)*2^(n+1)
错位相减得-Sn=2*2^1+1*2^2+1*2^3+1*2^4+…………+1*2……n-(n+1)*2^(n+1)
-Sn=1*2^1+1*2^2+1*2^3+1*2^4+…………+1*2……n-(n+1)*2^(n+1)+1*2^1
-Sn=2(2^n-1)-(n+1)*2^(n+1)+2
-Sn=2^(n+1)-2+2-(n+1)*2^(n+1)
-Sn=(1-n)*2^(n+1)
所以Sn=n*2^(n+1)