Bounded by a Hidden Sine

Problem

A sequence satisfies $a_0 = 0$ , $a_1 = \dfrac13$ , and

3a_{n+1} - 4a_n + 3a_{n-1} = 0 \qquad (n \ge 1).

Prove that $|a_n| < \dfrac12$ for every positive integer $n$ .

Answer

Solution

Difficulty	7/10
Topics	complex numbers, sequences

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