if q≥1 and x>−1 then: (1+x)^q ≥ (1+x)^(q−1) + x ≥ 1+qx


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Question Number 145191 by mathdanisur last updated on 03/Jul/21

$i f q ⩾ 1 a n d x > - 1 t h e n :$ ${(1 + x)}^{q} ⩾ {(1 + x)}^{q - 1} + x ⩾ 1 + q x$
	Answered by Olaf_Thorendsen last updated on 03/Jul/21

	${(1 + x)}^{q} = {(1 + x)}^{q - 1} (1 + x)$ $= {(1 + x)}^{q - 1} + x {(1 + x)}^{q - 1}$ $⩾ {(1 + x)}^{q - 1} + x$ $⩾ 1 + (q - 1) x + x = 1 + q x$
	Commented bymathdanisur last updated on 03/Jul/21

	$t h a n k y o u S e r, c o o l$
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