if-q-1-and-x-gt-1-then-1-x-q-1-x-q-1-x-1-qx-

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 by mathdanisur last updated on 03/Jul/21

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