数列﹛an﹜的通项式为an=1/(n²+2n),则S8=
问题描述：
数列﹛an﹜的通项式为an=1/(n²+2n),则S8=
答
∵an=1/(n²+2n)=1/n(n+2),
∴S8=1/1*3+1/2*4+1/3*5+1/4*6+1/5*7+1/6*8+1/7*9+1/8*10
=1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+……+1/8-1/10
=1+1/2-1/9-1/10
=58/45 .