Sum Of Reciprocal Of Perfect Powers

Calculus Level 3

\[\large 1+\dfrac{1}{2^4}+\dfrac{1}{3^4}+\dfrac{1}{4^4}+\ldots=\displaystyle \sum^{\infty}_{n=1}\dfrac{1}{n^4}= \, ? \]

Give your answer to 3 decimal places.

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