Soit U_n =((n−1)/(n^2 −5n+5)) avec n ∈ N. Montrer par la definition que U


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Question Number 163137 by mathocean1 last updated on 04/Jan/22

$S o i t U_{n} = \frac{n - 1}{n^{2} - 5 n + 5} a v e c n \in N .$ $M o n t r e r p a r l a d e f i n i t i o n q u e U_{n}$ $c o n v e r g e v e r s 0 .$
	Answered by puissant last updated on 04/Jan/22

	$S o i t ε > 0, c h e r c h o n s N_{ε} \in N / \forall n \in N,$ $n > N_{ε} \Rightarrow ∣ U_{n} ∣< ε .$ $e n e f f e t, o n a :$ $∣ U_{n} ∣=∣ \frac{n - 1}{n^{2} - 5 n + 5} ∣⩾∣ \frac{n}{n^{2} - 5 n + 5} ∣⩾∣ \frac{n}{n^{2}} ∣$ $n > N_{ε} \Rightarrow \frac{1}{n} < ε \Rightarrow n > \frac{1}{ε} .$ $p r e n d r e N_{ε} = E (\frac{1}{ε}) + 1 .$
	Commented by mathocean1 last updated on 10/Jan/22

	$t h a n k s .$
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