Question Number 145687 by mathdanisur last updated on 07/Jul/21
$${if}\:\:{q}\geqslant\mathrm{3}\:;\:{a}>-\mathrm{1}\:\:{then}: \\ $$$$\left(\mathrm{1}+{a}\right)^{\boldsymbol{{q}}} \:\geqslant\:\left(\mathrm{1}+\mathrm{2}{a}\right)\left(\mathrm{1}+{a}\right)^{\boldsymbol{{q}}-\mathrm{2}} \:\geqslant\:\mathrm{1}+{qa} \\ $$