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Proof WritingSuperchallengeInduction

Induction · Superchallenge problem

Define a1=1a_1 = 1 and an+1=an+1ana_{n+1} = a_n + \dfrac{1}{a_n}. Induction gives an2≥2n−1a_n^2 \ge 2n - 1. What is ⌊a100⌋\lfloor a_{100} \rfloor?