求数列{2n-1/2的n次方}的前n项和
问题描述:
求数列{2n-1/2的n次方}的前n项和
答
Sn=2-+2^2-(1/2)^2+2^3-(1/2)^3+…+2^n-(1/2)^n
=2+2^2+2^3+…+2^n-〔1/2+(1/2)^2+(1/2)^3+…+(1/2)^n〕
=2(2^n-1)/(2-1)-﹛1/2〔(1/2)^n-1〕﹜/(1/2-1)
=2^(n+1)-2-〔1-(1/2)^n〕
=2^(n+1)-2-1+(1/2)^n
=2^(n+1)+(1/2)^n-3