求和an=1/3n(n+1),求sn.

题目

求和an=1/3n(n+1),求sn.

答案

an=(1/3)[1/n-1/(n+1)]
sn=(1/3){(1/1-1/2)+(1/2-1/3)+.+[1/n-1/(n+1)]}
=(1/3)[1-1/(n+1)]
=1/3-1/3(n+1)