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The Basel Problem

14 Mar 2023

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Pietro Mengoli was an Italian mathematician and clergyman from Bologna, teaching at the University of Bologna [1]. He worked on infinite series and limits of geometric figures.

In 1650 he posed the following problem: What does the following summation converge to?

[\sum_{n=1}^{\infty} \frac{1}{n^2}]

It took almost 100 years for it to be solved. Euler provided a solution in 1735 which was correct but his proof lacked some formalism.

In this post we’ll discuss Euler’s proof to this problem and understand what parts it was missing. It’s my first post in celebration of $\pi$-day.

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