2016/095) If $\frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \cdots = \frac{\pi^4}{90}$

then  $\frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \cdots = ...$

Solution
Let $\frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \cdots = x$
$\frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \cdots = \frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \cdots + \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + \cdots$
or $\frac{\pi^4}{90} = x + \frac{1}{2^4}(\frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \cdots)$
$\frac{\pi^4}{90} = x + \frac{1}{16}\frac{\pi^4}{90}$
or $y = \frac{\pi^4}{96}$