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Kontes Terbuka Olimpiade Matematika - April 2017 - Bagian B Nomor 5

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Barisan $\{p_{n}\}, \{q_{n}\},\{r_{n}\}$ memenuhi $p_1=1, q_1=4, r_1=7$ dan $$p_{n+1}=q_{n}+\frac{6}{r_{n}}, q_{n+1}=r_{n}+\frac{6}{p_{n}}, r_{n+1}=p_{n}+\frac{6}{q_{n}}$$ untuk tiap $n\geq 1$. Buktikan bahwa $\max\{p_n,q_n,r_n\}\geq 2\sqrt{3n+\frac{5}{2}}$

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