Squeezed Toward One

★ 8/10Monotonicity Recursion sequences inequality

Problem

A sequence $\{a_n\}$ has $a_n > 0$ and

a_{n+1} + \frac{1}{a_n} < 2 \qquad \text{for all } n \in \mathbb{N}^*.

1. Prove that $a_{n+2} < a_{n+1} < 2$ . 2. Prove that $a_n > 1$ for all $n$ .

Answer

Solution

Difficulty	8/10
Topics	Monotonicity, Recursion, sequences, inequality

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