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finite_sum_of_complex_numbers [2015/06/20 16:21]
nikolaj
finite_sum_of_complex_numbers [2015/06/20 16:22]
nikolaj
Line 3: Line 3:
 | @#55CCEE: context ​    | @#55CCEE: $ (z_i) \in \mathrm{FinSequence}(\mathbb C)$ | | @#55CCEE: context ​    | @#55CCEE: $ (z_i) \in \mathrm{FinSequence}(\mathbb C)$ |
 | @#55CCEE: context ​    | @#55CCEE: $ n=\mathrm{length}((z_i)) $ | | @#55CCEE: context ​    | @#55CCEE: $ n=\mathrm{length}((z_i)) $ |
- 
 | @#FFBB00: definiendum | @#FFBB00: $\sum: \mathrm{FinSequence}(\mathbb C)\to \mathbb C$ | | @#FFBB00: definiendum | @#FFBB00: $\sum: \mathrm{FinSequence}(\mathbb C)\to \mathbb C$ |
 | @#FFBB00: definiendum | @#FFBB00: $\sum_{i=1}^n\ z_i:= \begin{cases} 0 & \mathrm{if}\ n=0\\\\ \left(\sum_{i=1}^{n-1}\ z_i\right)\ +\ z_n & \mathrm{else} \end{cases}$ | | @#FFBB00: definiendum | @#FFBB00: $\sum_{i=1}^n\ z_i:= \begin{cases} 0 & \mathrm{if}\ n=0\\\\ \left(\sum_{i=1}^{n-1}\ z_i\right)\ +\ z_n & \mathrm{else} \end{cases}$ |
  
-==== Discussion ====+-----
 === Theorem === === Theorem ===
 ^ $\sum_{k=1}^n z^k=\frac{1}{1-z}(1-z^{n+1})$ ^ ^ $\sum_{k=1}^n z^k=\frac{1}{1-z}(1-z^{n+1})$ ^
-==== Parents ====+ 
 +-----
 === Subset of === === Subset of ===
 [[Finite sum over a monoid]] [[Finite sum over a monoid]]
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