A Limit Hidden in a Recurrence

★ 8/10Limits calculus sequences Estimation Telescoping

Problem

A sequence has $a_1 = 1$ and

a_{n+1} = a_n + \frac{1}{2a_n}.

Evaluate

\lim_{n \to \infty}\left(a_n - \sqrt{n}\right).

Answer

Solution

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

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