MathDB

Upper and lower bound of sum and ln(n)

Source: China Second Round 2009 Problem 2

February 18, 2012

logarithmsinequalities proposedinequalities

Problem Statement

Let

n

be a positive integer. Prove that

-1<\sum_{k=1}^{n}\frac{k}{k^2+1}-\ln n\le\frac{1}{2}