An inequality
Posted: Wed Jul 12, 2017 6:18 pm
For $x > 0$, prove that
$$\left(\sum_{n=0}^\infty\frac{1}{(n+x)^2}\right)^2 \geq 2\,\sum_{n=0}^\infty\frac{1}{(n+x)^3}.$$
$$\left(\sum_{n=0}^\infty\frac{1}{(n+x)^2}\right)^2 \geq 2\,\sum_{n=0}^\infty\frac{1}{(n+x)^3}.$$