Apostol's Solution to the Basel problem

The Basel problem asks for the solution to the infinite series of the reciprocal squares: $$ \sum_{n=1}^\infty \frac 1 {n^2} = \, ? $$ As many other things in mathematics, it was first solved by Euler, who found that the solution was, incredibly, the transcendental value: $$ \frac{\pi^2}{6} $$ If you read through the linked Wikipedia page, you&rsquo;ll see many (quite beautiful) proofs, but they…