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Source: 1993 National High School Mathematics League, Exam One, Problem 15

February 28, 2020

Problem Statement

Positive sequence (an)n=0∞(a_n)_{n=0}^{\infty} satisfies that anan−2−an−1an−2=2an−1(n≥2),a0=a1=1\sqrt{a_na_{n-2}}-\sqrt{a_{n-1}a_{n-2}}=2a_{n-1}(n\geq2),a_0=a_1=1. Find ana_n.
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