1/3+1/15+1/35+1/63+1/99+...+1/(2n-1)(2n+1)
=1/2(1-1/3)+1/2(1/3-1/5)+...+1/2[1/(2n-1)-1/(2n+1)]
=1/2[1-1/(2n+1)]
=n/(2n+1)