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polynomial P(k) =k/(k + 1), k=0,...,2017, p(2018)=? (HOMC 2018 Ind. p14)

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January 31, 2020
algebrapolynomial

Problem Statement

Let P(x)P(x) be a polynomial with degree 20172017 such that P(k)=kk+1P(k) =\frac{k}{k + 1}, ∀k=0,1,2,...,2017\forall k = 0, 1, 2, ..., 2017 . Calculate P(2018)P(2018).
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