求数列{n+1/2的n次方}的前n项和

求数列{n+1/2的n次方}的前n项和
求数列{n+1/2的n次方}的前n项和

求数列{n+1/2的n次方}的前n项和
∵a[n]=n+1/2^n
∴S[n]=(1+1/2^1)+(2+1/2^2)+(3+1/2^3)+...+(n+1/2^n)
=(1+2+3+...+n)+(1/2^1+1/2^2+1/2^3+...+1/2^n)
=n(n+1)/2+(1/2)[1-(1/2)^n]/(1-1/2)
=n(n+1)/2+1-(1/2)^n