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MGO of SU : Colloquia

Friday Febuary 20 , 1:00 pm, Carnegie 300

The sum of \frac{1}{n^2} = \frac{\pi^2}{6} : an easier proof
Claudio DiMarco, Syracuse University

The Cauchy condensation test shows that series \sum_{n=1}^{\infty} \frac{1}{n^p} converges if and only if p>1. "Euler's series" is the above sum with p=2. It is a classical and important result that the sum of this series is \frac{\pi^2}{6} . We will present a simple "proof from the book" of this fact that requires only calculus. This is a welcome departure from the trappings the proof found in (blue) Rudin which relies on Parseval's theorem.