2010-21 Limit

Let \(a_1=0\), \(a_{2n+1}=a_{2n}=n-a_n\). Prove that there exists k such that \(\lvert a_k- \frac{k}{3}\rvert >2010\) and yet \(\lim_{n\to \infty} \frac{a_n}{n}=\frac13\).

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2010-21 Limit, 4.0 out of 5 based on 14 ratings