Let $(a_i)_{i\in \mathbb{N}}$ be a sequence with $a_1=\frac{3}2$ such that $$a_{n+1}=1+\frac{n}{a_n}$$Find $n$ such that $2020\le a_n <2021$
Source: The francophone mathematical olympiads P3
Tags: Sequence, algebra, Francophone
Let $(a_i)_{i\in \mathbb{N}}$ be a sequence with $a_1=\frac{3}2$ such that $$a_{n+1}=1+\frac{n}{a_n}$$Find $n$ such that $2020\le a_n <2021$