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Question Number 31523 by abdo imad last updated on 09/Mar/18
$${let}\:{give}\:{u}_{{n}} =^{{n}+\mathrm{1}} \sqrt{{n}+\mathrm{1}}\:\:−^{{n}} \sqrt{{n}}\: \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{convergence}\:{of}\:\left({u}_{{n}} \right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:{serie}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} {u}_{{n}} \\ $$