# Geome(trig)tric progression

Geometry Level 5

$\displaystyle \sum^{2016}_{n=1}\dfrac{1}{2^{n-1}}\tan \dfrac{\theta}{2^{n-1}}$

If the value of the above sum is in the form $$\frac{1}{2^{k}}\cot \frac{\theta}{2^{k}}-2\cot m\theta$$, where $$k$$, $$m \in \mathbb{N}$$, then find $$k+m$$.

×