Question Number 5513 by 314159 last updated on 17/May/16
$${If}\:{n}>\mathrm{1},\:{prove}\:{by}\:{mathematical}\:{induction}\:{that} \\ $$$${n}\left(\left({n}+\mathrm{1}\right)^{\frac{\mathrm{1}}{{n}}} −\mathrm{1}\right)\:<\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+…\frac{\mathrm{1}}{{n}}. \\ $$