Question Number 86672 by M±th+et£s last updated on 30/Mar/20
$${show}\:{proofs}\:{by}\:{induction},{that} \\ $$$$\frac{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +….+{x}_{{n}} }{{n}}\geqslant\left({x}_{\mathrm{1}} {x}_{\mathrm{2}} ….{x}_{{n}} \right)^{\frac{\mathrm{1}}{{n}}} \\ $$$$\forall{n}=\mathrm{2}^{{k}} ,{k}>\mathrm{1}\:{and}\:\left({x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,{x}_{\mathrm{3}} ,…..{x}_{{n}} \right)>\mathrm{0}. \\ $$