1/(n+1)(n+2)=1/(n+1)-1/(n+2)Sn=a1+a2+...+an=1/(2*3)+1/(3*4)+...+1/[n(n+1)]=1/2-1/3+1/3-1/4+...+1/n-1/(n+1)=1/2-1/(n+1)1/2-1/(n+1)=7/181/(n+1)=1/9n=8
思路：裂项相消……
