Sn=1/2^2-1+1/4^2-1+……+1/(2n)^2-1
=1/(1*3)+1/(3*5)+1/(5*7)+……+1/(2n-3)(2n-1)-1/(2n-1)(2n+1)
=(1/2)[1-1/3+1/3-1/5+……+1/(2n-3)-1/(2n-1)+1/(2n-1)-1/(2n+1)]
=(1/2)[1-1/(2n+1)]
=n/(2n+1)