If 1/(1⁴) + 1/(2⁴) + 1/(3⁴) + = (π⁴)/90, 1/(1⁴) + 1/(3⁴) + 1/(5⁴) + = α, 1/(2⁴) + 1/(4⁴) + 1/(6⁴) + = β, then (α)/(β) is equal to

Sequence and Series: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q204

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumSequence and Series179× since 2002

\frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \ldots = \frac{\pi^4}{90}

\frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \ldots = \alpha

\frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + \ldots = \beta

, then

\frac{\alpha}{\beta}

is equal to

JEE Main 2025 · April, Unspecified (session-level dataset) · Q204

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumSequence and Series179× since 2002

\frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \ldots = \frac{\pi^4}{90}

\frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \ldots = \alpha

\frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + \ldots = \beta

, then

\frac{\alpha}{\beta}

is equal to