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Define $(u_n)_{n\in\mathbb{N}^*}$:

$$u_1 =1 , u_{n+1}=1+\dfrac{n}{u_n}$$

Find an asymptotic equivalent of $u_n$ when $n\to+\infty$.

I guess that the answer should be $\sqrt{n}$, but I couldn't prove it...

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marked as duplicate by Did real-analysis Mar 5 '17 at 13:05

This question was marked as an exact duplicate of an existing question.

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You could try to show by induction that $\sqrt{n}<u_{n}<1+\sqrt{n}$ or something like that.

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