Etudiez la convergence de de la suite U_n =((1+cos(n)+2n)/(ni+(√((n+1)(n+2))))) ; n ∈ N. [study the convergence of U


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Question Number 164475 by mathocean1 last updated on 17/Jan/22

$E t u d i e z l a c o n v e r g e n c e d e d e l a$ $s u i t e U_{n} = \frac{1 + c o s (n) + 2 n}{n i + \sqrt{(n + 1) (n + 2)}}; n \in N .$ $[s t u d y t h e c o n v e r g e n c e o f U_{n}]$
	Answered by puissant last updated on 19/Jan/22

	$\lim_{n \to + \infty} U_{n} = \lim_{n \to + \infty} \frac{n (\frac{1}{n} + \frac{c o s (n)}{n} + 2)}{n (i + \sqrt{(1 + \frac{1}{n}) (1 + \frac{2}{n})}}$ $\Rightarrow \lim_{n \to + \infty} U_{n} = \frac{2}{i + 1} = \frac{2 (1 - i)}{\sqrt{2}} = \sqrt{2} - \sqrt{2} i .$
	Commented by mathocean1 last updated on 19/Jan/22

	$t h a n k s$
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