If 1/1⁴ + 1/2⁴ + 1/3⁴ + … ∞ = π⁴/90, 1/1⁴ + 1/3⁴ + 1/5⁴ + … ∞ = α… | JEE Main 2025 Mathematics PYQ

MCQEasyJEE Main 2025 · 8 April, Shift 2Sum of Series

If $\frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \dots \infty = \frac{\pi^4}{90},$ $\frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \dots \infty = \alpha,$ $\frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + \dots \infty = \beta,$ then $\frac{\alpha}{\beta}$ is equal to:

A
$23$
B
$15$
C
$14$
D
$18$

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