Sum of reciprocals of fourth powers

Calculus Level 2

Find the exact sum of n=11n4=1+124+134+144+ \sum_{n=1}^\infty \frac{1}{n^4}= 1+\frac{1}{2^4} + \frac{1}{3^4} + \frac{1}{4^4} + \cdots also known as ζ(4)\zeta(4), where ζ(s)\zeta(s) is the Riemann zeta function.


Hint: Follow Euler's famous solution of the Basel problem.

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