What does the following expression equal to
$$\sum\limits_{n=1}^\infty \cos(n\cdot\theta)=\text{?}$$
2025-01-13 02:22:36.1736734956
Infinite sum of cosine function
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$$\sum\limits_{n=1}^m\cos(n\theta)=\Re\sum\limits_{n=1}^me^{in\theta}=\Re\frac{e^{i(m+1)\theta}-e^{i\theta}}{e^{i\theta}-1}.$$
This expression has no limit.