Define a sequence $(a_n)_{n\in \mathbb{N}_0}$ recursively by $a_1=1$ and $$a_n=a_{n-1}+\frac{1}{a_{n-1}}$$ for $n\geq 2$. How can I prove that $12\leq a_{75}\leq 15$?
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A duplicate of this – Jyrki Lahtonen Apr 08 '19 at 22:02