设n为正整数,求证:1/1×3+1/3×5+...+1/(2n-1)(2n+1)
问题描述：
设n为正整数,求证:1/1×3+1/3×5+...+1/(2n-1)(2n+1)
答
:1/1×3=1/2(1-1/3)
1/3×5=1/2(1/3-1/5)
.
所以左边=1/2(1-1/3+1/3-1/5+...1/(2n-1)-1/(2n+1))
=1/2(1-1/(2n+1))