Question Number 161378 by KONE last updated on 22/Dec/21
$${determine},\:{pour}\:{tout}\:\alpha\in\mathbb{R},\:\:{la}\:{nature} \\ $$$$\:{de}\:{la}\:{serie}\:{de}\:{terme}\:{general} \\ $$$${U}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\left({k}^{\mathrm{2}} +\left({n}−{k}\right)^{\mathrm{2}} \right)^{\alpha} } \\ $$$${besoin}\:{d}'{aide}\:{svp} \\ $$$${please}\:{help}\:{me} \\ $$