Question

It is given that $\frac{1}{1^{4}}$+$\frac{1}{2^{4}}$+$\frac{1}{3^{4}}$+…..¥ = $\frac{\pi^{4}}{90}$ then

$\frac{1}{1^{4}} + \frac{1}{3^{4}} + \frac{1}{5^{4}} + ... + \infty$ is equal to –

• A. $\frac{\pi^{4}}{96}$
• B. $\frac{\pi^{4}}{45}$
• C. $\frac{89\pi^{4}}{90}$
• D. None

Answer 1

Answer: (A)

$\frac{\pi^{4}}{96}$

Answer 2

x = $\frac{1}{1^{4}}$+$\frac{1}{3^{4}}$+$\frac{1}{5^{4}}$+….¥

=$\left( \frac{1}{1^{4}} + \frac{1}{2^{4}} + \frac{1}{3^{4}} + ...\infty \right)$– $\left( \frac{1}{2^{4}} + \frac{1}{4^{4}} + ...\infty \right)$

= $\frac{\pi^{4}}{90}$– $\frac{1}{16}$ $\left( \frac{1}{1^{4}} + \frac{1}{2^{4}} + \frac{1}{3^{4}} + .....\infty \right)$

= $\frac{\pi^{4}}{90}$– $\frac{1}{16}$. $\frac{\pi^{4}}{90}$ = $\frac{\pi^{4}}{96}$.