1/n(n+1)=1/n+1/(n+1)
所以
原式=(1-1/2)+(1/2-1/3)+...+(1/8-1/9)+(1/9-1/10)
=1-1/2+1/2-1/3+...+1/8-1/9+1/9-1/10
=1-1/10
=9/10