解题的关键是一个分式变形.bn=1/(an*an+1)=1/[(2n-1)(2n+1)]=1/2{1/(2n-1) - 1/(2n+1)}Sn=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+...+1/2[ 1/(2n-1) - 1/(2n+1) ]=1/2*[1- 1/(2n+1)]=(1/2)*(2n/2n+1)=n/(2n+1)...