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Find limit, recurrence relation

Source: 2017 South Korea USCM P3

August 15, 2020
real analysislimitrecurrence relationcollege contests

Problem Statement

Sequence {an}\{a_n\} defined by recurrence relation an+1=1+n2ana_{n+1} = 1+\frac{n^2}{a_n}. Given a1>1a_1>1, find the value of lim⁡n→∞ann\lim\limits_{n\to\infty} \frac{a_n}{n} with proof.
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