1/3+1/15+1/35+1/63+.+1/(2n-1)(2n+1)
=1/2*[1-1/3+1/3-1/5+1/5-1/7+.+1/(2n-1)-1/(2n+1)]
=1/2*[1-1/(2n+1)]
=n/(2n+1)