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### Basel problem

The Basel problem asks for the exact value of the sum

##### Explanation

We start with the power series for the sine and divide through by *x* and obtain

The zeroes of this function are integer multiples of π, so the points *x* = *n* · π for *n* = ±1, ±2, ±3, ... . The factorisation theorem gives

what you can convert to

The multiplication of these factors show a clear pattern

We only continue with the coefficients of *x*^{2} and find

In the original series we can see that the coefficient of *x*^{2} equals there

and so applies

so that

##### Additional information

The first calculation of this probem from 1644 was given by Leonhard Euler in 1735.