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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] (current)nikolaj Both sides previous revision Previous revision 2015/06/20 16:22 nikolaj 2015/06/20 16:21 nikolaj 2014/03/21 11:11 external edit2014/01/29 19:55 nikolaj 2014/01/29 19:55 nikolaj 2013/12/21 19:57 external edit2013/09/09 15:56 nikolaj 2013/09/08 16:05 nikolaj 2013/09/08 15:48 nikolaj 2013/09/07 19:43 nikolaj 2013/09/07 19:39 nikolaj created 2015/06/20 16:22 nikolaj 2015/06/20 16:21 nikolaj 2014/03/21 11:11 external edit2014/01/29 19:55 nikolaj 2014/01/29 19:55 nikolaj 2013/12/21 19:57 external edit2013/09/09 15:56 nikolaj 2013/09/08 16:05 nikolaj 2013/09/08 15:48 nikolaj 2013/09/07 19:43 nikolaj 2013/09/07 19:39 nikolaj created 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]]