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Find the exact sum of ∑n=1∞1n4=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 n=1∑∞n41=1+241+341+441+⋯ also known as ζ(4)\zeta(4)ζ(4), where ζ(s)\zeta(s)ζ(s) is the Riemann zeta function.
Hint: Follow Euler's famous solution of the Basel problem.
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