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Question Number 31417 by abdo imad last updated on 08/Mar/18
$${let}\:{give}\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}}\:−{ln}\left({n}\right) \\ $$ $$\left.\mathrm{1}\right)\:{prove}\:{that}\:{u}_{{n}} \:{is}\:{convergent}\: \\ $$ $$\left.\mathrm{2}\right)\:{if}\:\:\:\gamma={lim}_{{n}\rightarrow\infty} {u}_{{n}} \:\:{prove}\:{the}\:\mathrm{0}<\gamma<\mathrm{1}\:. \\ $$