已知数列an中,an=1/(n(n+1)×(n+2)),则lim(n趋向于无限大)Sn的值

问题描述:

已知数列an中,an=1/(n(n+1)×(n+2)),则lim(n趋向于无限大)Sn的值

an=(1/2)[1/n(n+1)-1/(n+1)(n+2)]
所以Sn=1/2[1/1*2-1/2*3+1/2*3-1/3*4+……+1/n(n+1)-1/(n+1)(n+2)]
=1/2[1/2-1/(n+1)(n+2)]
n趋于无穷则趋于0
所以极限=1/2*1/2=1/4