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src/content/posts/math-examples.md

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+---
+title: "Math Examples"
+description: "REEEEEE"
+pubDate: 2024-06-08
+tags:
+    - "Gaybo"
+---
+
+Some simple mathematical expressions:
+
+$$ \sqrt{3x-1}+(1+x)^2 $$
+
+$$\frac{ax^2+bx+c}{(a+b)^2}=0$$
+
+$$f(x) = \pm A \sin\left(\frac{2\pi}{4} + \theta\right)$$
+
+More complicated examples (from [KateX home page](https://katex.org)):
+
+$$\displaystyle \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }$$
+
+$$\displaystyle \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$$
+
+$$\displaystyle {1 +  \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots }= \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for }\lvert q\rvert<1.$$