Finite geometric sums $\sum r^ke^{ik\phi}$, $\sum r^k\cos k\phi$ and $\sum r^k\sin k\phi$

Compute the following series: (a) \(\sum _ { k = 0 } ^ { n } r ^ { k } e ^ { i k \phi } ,\) (b) \(\sum _ { k = 0 } ^ { n } r ^ { k } \cos k \phi ,\) (c) \(\sum _ { k = 0 } ^ { n } r ^ { k } \sin k \phi .\)