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Infinite geometric series
Function
| definition | $Q_\infty: \{z\in{\mathbb C}\mid \vert{z}\vert<1\}\to\mathbb C$ |
| definition | $Q_\infty(z):=\sum_{k=0}^\infty z^k $ |
$Q_\infty(z)=\dfrac{1}{1-z}$
Theorems
$1+\dfrac{1}{z}=-1+\sum_{k=0}^\infty\left(\dfrac{1}{1+z}\right)^k$
References
Wikipedia: Geometric series, Geometric progression
Context
Related
