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...
Finding equivalent of an iterative sequence
1
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real-analysis
sequences-and-series
asymptotics
1 Answers
-1
You could try to show by induction that $\sqrt{n}