# Evaluating a summation

Calculus Level 3

If $\sum \limits_{k=1}^{101} \frac{(-1)^{k-1} \binom{100}{k-1}}{k+1} = \frac{a}{b}$ for some coprime positive integers $$a$$ and $$b$$, find the last three digits of $$a+b$$.

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