A good problem for a test.

Calculus Level 4

$\large \lim_{x \to 0} \frac{2017 - \sum_{k=1}^{2017} \cos kx}{x^2}$

The above limit can be expressed in the form $\dfrac{4035a(a+1)}{b}$ , where $a, b \in \mathbb{Z}^+$ . Find $a + b$ .

Note. The intention is for you to solve the problem without L'Hopital's rule or Taylor Series. Think Calculus I, limits unit, before you learned differentiation.