JEE Mains · Maths · STD 11 - 8. sequence and series
\(\begin{aligned}
& \text { If } \frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}+\ldots . . \infty=\frac{\pi^4}{90}, \\
& \frac{1}{1^4}+\frac{1}{3^4}+\frac{1}{5^4}+\ldots . . \infty=\alpha, \\
& \frac{1}{2^4}+\frac{1}{4^4}+\frac{1}{6^4}+\ldots . \infty=\beta,
\end{aligned}\)
then \(\frac{\alpha}{\beta}\) is equal to
- A 23
- B 18
- C 15
- D 14
Answer & Solution
Correct Answer
(C) 15
Step-by-step Solution
Detailed explanation
If \(\frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}+\ldots . . \infty=\frac{\pi^4}{90}....(i)\) \(\begin{aligned} & \beta=\frac{1}{2^4}+\frac{1}{4^4}+\frac{1}{6^4}+\ldots, \\ & =\frac{1}{16}\left[\frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}+\ldots . .\right],\end{aligned}\)…
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