求和1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)*(2n+1))
问题描述：
求和1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)*(2n+1))
求详解!
答
1/(1*3)+1/(3*5)+1/(5*7)+...+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)]
=1/2*2n/(2n+1)
=n/(2n+1)