数列2又1/3,4又1/9,6又1/27.2n+1/3^n的前N项和

问题描述:

数列2又1/3,4又1/9,6又1/27.2n+1/3^n的前N项和


Sn=(2+1/3)+(4+1/9)+...+(2n+1/3^n)
=(2+4+...+2n)+(1/3+1/9+1/3^n)
=(2+2n)n/2+1/3(1-1/3^n)/(1-1/3)
=(n+1)n+1/2(1-1/3^n)
=n²+n+1/2-1/[2*3^n].