# Brainstorming cosine series

Geometry Level 4

$\large \sum_{k=1}^{1007} \left(\cos\left(\dfrac{\pi{k}}{1007}\right)\right)^{2014}$

If the value of the sum above is of the form $$\dfrac{a+b\dbinom{a}{b}}{2^a}$$, where $$a=2b$$, find $$a+b$$.


Notation: $$\dbinom MN = \dfrac {M!}{N! (M-N)!}$$ denotes the binomial coefficient.

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