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An inequality

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