Question Number 200759 by brahim_mekkaoui last updated on 23/Nov/23
$$\mathrm{let}\:\mathrm{u}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}}{\mathrm{k}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} }\:\mathrm{for}\:\mathrm{n}\in\mathbb{N}_{>\mathrm{0}} \:\: \\ $$$$\mathrm{show}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}_{>\mathrm{0}} } \mathrm{is}\:\mathrm{increasing}. \\ $$