Question

一乘三分之一加三乘五分之一加五乘七分之一加······(2n-1)(2n+1)分之一 求和

Answer 1

1/(1×3) +1/(3×5)+ 1/(5×7)+...+1/[(2n-1)(2n+1)]
=½×[1- 1/3 +1/3- 1/5+ 1/5- 1/7+...+1/(2n-1) -1/(2n+1)]
=½×[1- 1/(2n+1)]
=n/(2n+1)