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Let $a_1,$ $a_2,$ $\dots$ be a sequence of real numbers such that for all positive integers $n,$ \[\sum_{k = 1}^n a_k \left( \frac{k}{n} \right)^2 = 1.\]Find the smallest $n$ such that $a_n < \frac{1}{2018}.$

 Aug 25, 2021
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The smallest n such that a_n < 1/2018 is 45.

 Aug 25, 2021

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