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Let $p(x)$ be a polynomial of degree 5 such that \[p(n) = \frac{n}{n^2 - 1}\]for $n = 2, 3, 4, \dots, 7$. Find $p(8).$

 Sep 23, 2021
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By Lagrange Interpolation, p(8) = 5/28.

 Sep 23, 2021

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