Question

如何求数列前n项和极限，谢谢

Answer 1

选C
用列项相消法
1/[(n+2)^2-1]=1/[(n+1)(n+3)]=1/2[1/(n+1)-1/(n+3)]

追问

但是Sn=1/2*(1/2-1/4+1/3-1/5+1/4-1/6+...+1/n+1-1/n+3)，似乎消不掉吧？

追答

只有第一项的前两项和第二项的后两项没消去
Sn=1/2*[1/2+1/3+1/4+1/5+···+1/(n+1)-(1/3+1/4+1/5+1/6+···+1/(n+1)+1/(n+2)+1/(n+3))]
=1/2[1/2+1/3-1/(n+2)-1/(n+3)]
再取极限即可