Infinite series with cos in numerator How do you evaluate this series?
$$\sum_{i=1}^{\infty}\frac{\cos i}{2^i}$$
It's absolutely convergent by comparison to the geometric series. But the $\cos$ is tripping me up. I've tried differentiating in order to go through the $\cos$ -> $\sin$ -> $\cos$ route, but that gives me different powers of 2 in the denominator. Any ideas?

Hint. One may write, for $|q|<1$, $\alpha \in \mathbb{R}$,
$$
\sum_{n=1}^{\infty} q^n \cos(n\alpha)=\Re \sum_{n=1}^{\infty} (qe^{i\alpha})^n =\Re\: \frac{qe^{i\alpha}}{1-qe^{i\alpha}}
$$ where we have used the standard evaluation of a geometric series.
