prove that the arithmetic mean of a sequence is greater or equal to the geometric mean. that is ((a + b)/2) ≥ (√(ab))


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Question Number 72693 by Rio Michael last updated on 31/Oct/19

$p r o v e t h a t t h e a r i t h m e t i c m e a n o f a s e q u e n c e$ $i s g r e a t e r o r e q u a l t o t h e g e o m e t r i c m e a n .$ $t h a t i s$ $\frac{a + b}{2} ⩾ \sqrt{a b}$
	Answered by MJS last updated on 31/Oct/19

	$a + b ⩾ 2 \sqrt{a b}$ ${(a + b)}^{2} ⩾ 4 a b$ $a^{2} + 2 a b + b^{2} ⩾ 4 a b$ $a^{2} - 2 a b + b^{2} ⩾ 0$ ${(a - b)}^{2} ⩾ 0$ $always true$
	Commented by Rio Michael last updated on 31/Oct/19

	$t h a n k y o u s i r$
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