The geometric sum

$$\sum_{i=0}^n k^i = \frac{1-k^{n+1}}{1-k}$$

is a continuous function of $k$ on $\mathbb{R}^+$ whose limit as $k\to 0$ is $n+1$, i.e. the value of the left-hand side sum for $k=0$.

For this page to display the math, I would need to install a plugin (MathJax of KaTeX for example) but this requires to get a non-free subscriptionâ€¦

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