Add finite and infinite series formulae

Author: kevinlinxc

README.md

@@ -69,6 +69,6 @@ Then, repeat everything after step 5.
 ## Top contributors
 (This could eventually be a nicely presented leaderboard on the site.)
 
-kevinlinxc: 36 formulas
+kevinlinxc: 37 formulas
 
 

content/formulas/finite-infinite-series/index.md

@@ -0,0 +1,26 @@
+---
+title: "Finite and Infinite Geometric Series"
+description: "The simplified formulas for finite and infinite geometric series."
+summary: "The simplified formulas for finite and infinite geometric series."
+tags: ["math"]
+date: 2023-02-26
+latex: S_n = \frac{a(1-r^n)}{1-r}
+---
+{{< katex >}}
+
+## Finite Geometric Series
+For a series of the form \\( \small a, ar, ar^2, ar^3, \ldots\\), the sum of the first \\(\small n\\) terms is
+
+$$S_n = \sum_{n=0}^{N} ar^n = \frac{a(1-r^N)}{1-r}$$
+
+where \\(r \neq 1 \\) is the common ratio.
+
+## Infinite Geometric Series
+If the magnitude of \\(r\\) is less than \\(1\\), the sum of the infinite series is
+
+$$S_{\infty} = \sum_{n=0}^{\infty} ar^n = \frac{a}{1-r}$$
+
+
+## Sources
+- [Wikipedia](https://en.wikipedia.org/wiki/Geometric_series)
+- [Amsi.org.au](https://amsi.org.au/ESA_Senior_Years/SeniorTopic1/1d/1d_2content_5.html)