A Sequence That Grows Like a Root

★ 7/10sequences Estimation Telescoping inequality

Problem

A sequence satisfies $a_1 = 1$ and

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

Prove that $a_{2015} > 63$ .

Answer

Solution

Difficulty	7/10
Topics	sequences, Estimation, Telescoping, inequality

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