A good problem for a test.

Calculus Level 4

limx02017k=12017coskxx2\large \lim_{x \to 0} \frac{2017 - \sum_{k=1}^{2017} \cos kx}{x^2}

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

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