求数列之和
问题描述：
求数列之和
1/S1+1/S2+1/S3+```````+1/Sn
的值
我知道 Sn＝n^2+2n
怎么求啊
答
Sn＝n^2+2n
1/Sn=1/(n^2+2n)=1/n(n+2)=1/2*[1/n-1/(n+2)]
1/S1+1/S2+1/S3+```````+1/Sn=1/2×[(1-1/3)+(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+…+1/n-1/(n+2)]
=1/2×[1+1/2-1/(n+1)-1/(n+2)]
=3/4-(2n+3)/[2(n+1)(n+2)]