数列1又1/3,2又1/9,3又1/27,4又1/81,…的前n项和是

题目

数列1又1/3,2又1/9,3又1/27,4又1/81,…的前n项和是

答案

=1+1/3+2+1/9……+n+1/3^n
=1+2……+n+1/3+1/9……+1/3^n
=n(n+1)/2+(1/3){1-(1/3)^n}/{1-(1/3)}
=n(n+1)/2+(1/2){1-(1/3)^n}