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p(2023) =? if p(k) =1/(k+1)

Source: Puerto Rico TST 2023.2.3

March 24, 2024
algebrapolynomial

Problem Statement

Let p(x)p(x) be a polynomial of degree 20222022 such that: p(k)=1k+1   for    k=0,1,...,2022p(k) =\frac{1}{k+1}\,\,\, \text{for }\,\,\, k = 0, 1, . . . , 2022 Find p(2023)p(2023).
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