# MARKDPWN-EXAMPLE

$$
\Bigg \langle 3x+7 \bigg \rangle
$$

$$
y  = 1 + & \left(  \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \ldots \right. \\
& \quad \left. + \frac{1}{x^{n-1}} + \frac{1}{x^n} \right)
$$

$$
F = G \left( \frac{m\_1 m\_2}{r^2} \right)
$$

$$
\left\[  \frac{ N } { \left( \frac{L}{p} \right)  - (m+n) }  \right]
$$

$$\begin{matrix} 2 & 2 & 3\ 3 & 2 & 4\ \end{matrix}$$

$$\begin{pmatrix} 2 & 2 & 3\ 3 & 2 & 4\ \end{pmatrix}$$

$$\begin{vmatrix} 2 & 2 & 3\ 3 & 2 & 4\ \end{vmatrix}$$

$$\begin{Vmatrix} 2 & 2 & 3\ 3 & 2 & 4\ \end{Vmatrix}$$

$$\begin{bmatrix} 2 & 2 & 3\ 3 & 2 & 4\ \end{bmatrix}$$

$$\begin{Bmatrix} 2 & 2 & 3\ 3 & 2 & 4\ \end{Bmatrix}$$

$$\begin{cases} x^2 + 2x +2 = 0\ x^3 + 3x^2 +5 = 0\   \end{cases}$$

$$
\begin{array}{c}
a+b\\
\[f,g]\\
m+n
\end{array}
$$

$$|\vec{A}|=\sqrt{A\_x^2 + A\_y^2 + A\_z^2}$$

$$\vec{A}=ABC+DEF$$

$$\sum\_{i=1}^{10} t\_i$$

$$\int\_0^\infty$$

$$\int\_0^\infty \mathrm{e}^{-x},\mathrm{d}x$$

Let $( \mathcal{T} )$ be a topological space, a basis is defined as

$$
\mathcal{B} = {B\_{\alpha} \in \mathcal{T}, |,  U = \bigcup B\_{\alpha} \forall U \in \mathcal{T} }
$$

$$$
$$
\begin{align\*}
RQSZ \\
\mathcal{RQSZ} \\
\mathfrak{RQSZ} \\
\mathbb{RQSZ}
\end{align\*}
$$$

$$
\begin{align\*}
3x^2 \in R \subset Q \\
\mathnormal{3x^2 \in R \subset Q} \\
\mathrm{3x^2 \in R \subset Q} \\
\mathit{3x^2 \in R \subset Q} \\
\mathbf{3x^2 \in R \subset Q} \\
\mathsf{3x^2 \in R \subset Q} \\
\mathtt{3x^2 \in R \subset Q}
\end{align\*}
$$

$$\begin{equation\*} \sum\_{i=1}^n i = \left(\sum\_{i=1}^{n-1} i\right) + n = \frac{(n-1)(n)}{2} + n = \frac{n(n+1)}{2} \end{equation\*}$$

\displaystyle \bigg|\bigg| + \big|x - |1 - a| + \big| = 0

|                      |                                           |
| -------------------- | ----------------------------------------- |
| a\_{n\_i}            | {$$displaystyle a\_{n\_{i}}$$}            |
| \int\_{i=1}^n        | {$$displaystyle \int \_{i=1}^{n}$$}       |
| \sum\_{i=1}^{\infty} | {$$displaystyle \sum \_{i=1}^{\infty }$$} |
| \prod\_{i=1}^n       | {$$displaystyle \prod \_{i=1}^{n}$$}      |
| \cup\_{i=1}^n        | {$$displaystyle \cup \_{i=1}^{n}$$}       |
| \cap\_{i=1}^n        | {$$displaystyle \cap \_{i=1}^{n}$$}       |
| \oint\_{i=1}^n       | {$$displaystyle \oint \_{i=1}^{n}$$}      |
| \coprod\_{i=1}^n     | {$$displaystyle \coprod \_{i=1}^{n}$$}    |

$$
\binom{n}{k} = \frac{n!}{k!(n-k)!}
$$

$$f(x)=\frac{P(x)}{Q(x)} \ \ \textrm{and} \ \ f(x)=\textstyle\frac{P(x)}{Q(x)}$$

$$\frac{1+\frac{a}{b}}{1+\frac{1}{1+\frac{1}{a}}}$$

Now a wild example

$$
a\_0+\cfrac{1}{a\_1+\cfrac{1}{a\_2+\cfrac{1}{a\_3+\cdots}}}
$$

$$
\newcommand\*{\contfrac}\[2]{%
{
\rlap{$\dfrac{1}{\phantom{#1}}$}%
\genfrac{}{}{0pt}{0}{}{#1+#2}%
}
}
$$

$$
a\_0 +
\contfrac{a\_1}{
\contfrac{a\_2}{
\contfrac{a\_3}{
\genfrac{}{}{0pt}{0}{}{\ddots}
}}}
$$

$$
\begin{equation} \label{eq1}
\begin{split}
A & = \frac{\pi r^2}{2} \\
& = \frac{1}{2} \pi r^2
\end{split}
\end{equation}
$$

$$
\begin{multline\*}
p(x) = 3x^6 + 14x^5y + 590x^4y^2 + 19x^3y^3\\

* 12x^2y^4 - 12xy^5 + 2y^6 - a^3b^3
  \end{multline\*}
  $$

$$
\begin{align\*}
2x - 5y &=  8 \\
3x + 9y &=  -12
\end{align\*}
$$

$$
\begin{align\*}
x&=y           &  w &=z              &  a&=b+c\\
2x&=-y         &  3w&=\frac{1}{2}z   &  a&=b\\
-4 + 5x&=2+y   &  w+2&=-1+w          &  ab&=cb
\end{align\*}
$$

$$
\begin{gather\*}
2x - 5y =  8 \\
3x^2 + 9y =  3a + c
\end{gather\*}
$$

Testing notation for limits

$$
\lim\_{h \to 0 } \frac{f(x+h)-f(x)}{h}
.
$$

This operator changes when used alongside text ( \lim\_{h \to 0} (x-h) ).

$$
S = { z \in \mathbb{C}, |, |z| < 1 } \quad \textrm{and} \quad S\_2=\partial{S}
$$

$$
\begin{align\*}
f(x) &= x^2! +3x! +2 \\
f(x) &= x^2+3x+2 \\
f(x) &= x^2, +3x, +2 \\
f(x) &= x^2: +3x: +2 \\
f(x) &= x^2; +3x; +2 \\
f(x) &= x^2\ +3x\ +2 \\
f(x) &= x^2\quad +3x\quad +2 \\
f(x) &= x^2\qquad +3x\qquad +2
\end{align\*}
$$

$$\sum\_{n=1}^{\infty} 2^{-n} = 1$$

$$\sum\_{n=1}^{\infty} 2^{-n} = 1$$

$\lim\_{x\to\infty} f(x)$

$$\lim\_{x\to\infty} f(x)$$

Depending on the value of $x$ the equation ( f(x) = \sum\_{i=0}^{n} \frac{a\_i}{1+x} ) may diverge or converge.

$$f(x) = \sum\_{i=0}^{n} \frac{a\_i}{1+x}$$

In-line maths elements can be set with a different style: (f(x) = \displaystyle \frac{1}{1+x}). The same is true the other way around:

$$
\begin{eqnarray\*}
f(x) = \sum\_{i=0}^{n} \frac{a\_i}{1+x} \\
\textstyle f(x) = \textstyle \sum\_{i=0}^{n} \frac{a\_i}{1+x} \\
\scriptstyle f(x) = \scriptstyle \sum\_{i=0}^{n} \frac{a\_i}{1+x} \\
\scriptscriptstyle f(x) = \scriptscriptstyle \sum\_{i=0}^{n} \frac{a\_i}{1+x}
\end{eqnarray\*}
$$

Let $( \mathcal{T} )$ be a topological space, a basis is defined as

$$
\mathcal{B} = {B\_{\alpha} \in \mathcal{T}, |,  U = \bigcup B\_{\alpha} \forall U \in \mathcal{T} }
$$