Indices, Fractions, Series and Pi

Level 2

If the infinite series 1 + 1 2 4 + 1 3 4 + 1 4 4 + 1 5 4 + . . . = π x y 1 + \frac {1}{2^4} + \frac {1}{3^4} + \frac {1}{4^4} + \frac {1}{5^4} + ... = \frac {\pi^x}{y} , what is 2 x y 2xy ?


The answer is 720.

Sharky Kesa by Sharky Kesa , 19, United Kingdom

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1 solution

The answer of π x y \frac{\pi^{x}}{y} is a result of applying the Riemann Zeta function for the value of 4 4 . You get x = 4 x=4 and y = 90 y=90 . Thus, 2 x y 2xy = = 720 \boxed{720}

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