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Calculus Level 4

1 1 4 + 1 2 4 + 1 3 4 + … = π p i \large \dfrac{1}{1^4}+\dfrac{1}{2^4}+\dfrac{1}{3^4}+ \ldots = \dfrac{\pi^p}{i}

Find p + i p+i .

Note: i i is a integer not imaginary number.

Inspiration


The answer is 94.

Anish Harsha by Anish Harsha , 20, India

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1 solution

This is a famous result. ζ ( 4 ) = π 4 90 \zeta(4)=\dfrac{\pi^4}{90} .

Therefore p + i = 90 + 4 = 94 p+i=90+4=\boxed{94} .

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