# Polynomial Evaluation

$f(x)$ is a polynomial with degree equal to 100. It satisfies $f(n) = \frac {1} {n}$, for all integers $n$ between 1 and 101, inclusive. $f(102)$ is a fraction and has the form $\frac {a} {b}$, where $a$ and $b$ are coprime integers. What is $a + b?$

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