已知数列an=1/[n(n+1)(n+2)],求Sn的极限

题目

已知数列an=1/[n(n+1)(n+2)],求Sn的极限

答案

An=1/2*[1/n(n+1)-1/(n+1)(n+2)]
Sn=1/2*[1/2-1/6+1/6-1/12+.+1/n(n+1)-1/(n+1)(n+2)]
=1/2*[1/2-1/(n+1)(n+2)]