Finding equivalent of an iterative sequence 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...
You could try to show by induction that $\sqrt{n}&lt;u_{n}&lt;1+\sqrt{n}$ or something like that.
You could try to show by induction that $\sqrt{n}&lt;u_{n}&lt;1+\sqrt{n}$ or something like that.