根据题意通项an=(1+2+3+.+n)/(n+1)=[(1+n)n/2]/(n+1)=n/2裂项：1/(an*an+1)=4/[n(n+1)]=4[1/n-1/(n+1)] {1/(an*an+1)}的前n项和Tn=4[1-1/2+1/2-1/3+1/3-1/4+.+1/n-1/(n+1)]=4[1-1/(n+1)]n-->∞时,Tn-->4...