An algebra problem by Steven Lee

Algebra Level 3

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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