An algebra problem by Steven Lee

Algebra Level 4

Consider an \(n^\text{th}\) degree polynomial \(p(x)\) that satisfies the following condition:

\[p(k) = \frac{k}{k+1}, ~~k = 0, 1, 2, 3, ..., n .\]

Find the value of \(p(n+1)\) when \(n = 101.\)

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