An algebra problem by Steven Lee

Algebra Level 3

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

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

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

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