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if-x-gt-1-q-n-2-GIF-then-1-x-q-1-nx-1-q-n-x-1-qx-




Question Number 148262 by mathdanisur last updated on 26/Jul/21
if  x>−1  ;  [q]=n≥2  ;  [∗]-GIF  then:  (1+x)^q  ≥ (1+nx)(1+(q-n)x) ≥ 1+qx
$${if}\:\:{x}>−\mathrm{1}\:\:;\:\:\left[{q}\right]={n}\geqslant\mathrm{2}\:\:;\:\:\left[\ast\right]-{GIF}\:\:{then}: \\ $$$$\left(\mathrm{1}+{x}\right)^{\boldsymbol{{q}}} \:\geqslant\:\left(\mathrm{1}+{nx}\right)\left(\mathrm{1}+\left({q}-{n}\right){x}\right)\:\geqslant\:\mathrm{1}+{qx} \\ $$

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