===== Finite sum of complex numbers =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $ (z_i) \in \mathrm{FinSequence}(\mathbb C)$ |
| @#55CCEE: context     | @#55CCEE: $ n=\mathrm{length}((z_i)) $ |
| @#FFBB00: definiendum | @#FFBB00: $\sum: \mathrm{FinSequence}(\mathbb C)\to \mathbb C$ |
| @#FFBB00: definiendum | @#FFBB00: $\sum_{i=1}^n\ z_i:= \begin{cases} 0 & \mathrm{if}\ n=0\\\\ \left(\sum_{i=1}^{n-1}\ z_i\right)\ +\ z_n & \mathrm{else} \end{cases}$ |

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=== Theorem ===
^ $\sum_{k=1}^n z^k=\frac{1}{1-z}(1-z^{n+1})$ ^

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=== Subset of ===
[[Finite sum over a monoid]]