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](https://www.tinkutara.com/question/Q148262.png)
$${if}\:\:{x}>−\mathrm{1}\:\:;\:\:\left[{q}\right]={n}\geqslant\mathrm{2}\:\:;\:\:\left[\ast\right]-{GIF}\:\:{then}: \\ $$$$\left(\mathrm{1}+{x}\right)^{\boldsymbol{{q}}} \:\geqslant\:\left(\mathrm{1}+{nx}\right)\left(\mathrm{1}+\left({q}-{n}\right){x}\right)\:\geqslant\:\mathrm{1}+{qx} \\ $$