证明：数列n除以2n+1是递减数列

题目

证明：数列n除以2n+1是递减数列

答案

证明：考察a(n)和a(n+1)
a(n)-a(n+1)
=n / (2n+1) - (n+1) / (2n+3)
=[n (2n+3) - (n+1)(2n+1)] / (2n+1)(2n+3)
=-1 / (2n+1)(2n+3)