An Asymptotic Ratio

★ 8/10Limits sequences Estimation Telescoping

Problem

A sequence $\{a_n\}$ has $a_1 = 1$ and

a_{n+1} = a_n + \frac{1}{a_n} \qquad (n \in \mathbb{N}^*).

Find

\lim_{n \to +\infty} \frac{a_n}{\sqrt{n}}.

Answer

Solution

Difficulty	8/10
Topics	Limits, sequences, Estimation, Telescoping

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