IMC 2011 · Problem 3

Day 218th IMC · Blagoevgrad, Bulgaria

Statement

Determine the value of

n=1ln(1+1n)ln(1+12n)ln(1+12n+1).\sum_{n=1}^{\infty} \ln\left( 1 + \frac{1}{n} \right) \cdot \ln\left( 1 + \frac{1}{2n} \right) \cdot \ln\left( 1 + \frac{1}{2n+1} \right).

Official solution

Hidden so you can work on the problem first.