IMC 2015 · Problem 6

Day 222nd IMC · Blagoevgrad, Bulgaria

Statement

Prove that

n=11n(n+1)<2.\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}\,(n+1)} < 2.

Official solution

Hidden so you can work on the problem first.

Proposed by Ivan Krijan, University of Zagreb.