1/1x3+1/3x5+1/5x7+...+1/(2n+1)(2n-1)
=[1-1/3+1/3-1/5+1/5-1/7+……+1/(2n-1)-1/(2n-1)]÷2
=[1-1/(2n+1)]÷2
=2n/(2n+1)÷2
=n/(2n+1)