Prove by recurrence that (1/(n!))≤(1/2^(n−1) ), ∀n≥1.


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Question Number 160539 by LEKOUMA last updated on 01/Dec/21

$P r o v e b y r e c u r r e n c e t h a t$ $\frac{1}{n!} ⩽ \frac{1}{2^{n - 1}}, \forall n ⩾ 1 .$
	Answered by TheSupreme last updated on 01/Dec/21

	$n = 1$ $1 ⩽ 1$ $i f \frac{1}{n!} ⩽ \frac{1}{2^{n - 1}} \to \frac{1}{(n + 1)!} ⩽ \frac{1}{2^{n}}$ $\frac{1}{(n + 1)} \frac{1}{n!} ⩽ \frac{1}{(n + 1)} \frac{1}{2^{n - 1}} ⩽ \frac{1}{2^{n}}$ $\frac{1}{n + 1} ⩽ \frac{1}{2} \to n ⩾ 1$
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