[22.03][PP]

\documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}

\usepackage{polski}
\usepackage{lipsum}

%opening
\title{}
\author{}

%/uczymy się matematyki...

\begin{document}
\noindent
Tryb Matematyczny
\( x^{50} \) %\potęga

 $ a_2 $ %\index dolny

 \begin{math}
\frac{a^2 - b^2}{i-2}
\end{math}

$\frac{x}{y}$
${x}\over{y}$
nie eksponowany
ala


$$
\lim_n{ \to \infty}
\prod_{aaa}^{www}
\sum_{k=1}^{n=100} \frac{1}{k^2}
= \frac{\pi^2}{6} \alpha\sigma\Omega\omega
$$calka $$\int_{x=1}^{n}=\int\limits_{x=1}^{n}
$$
ma kota
\noindent
wzor eksponowany $x$


\begin{equation}
\lim_n{ \to \infty}
\prod_{aaa}^{www}
\sum_{k=1}^{n=100} \frac{1}{k^2}
= \frac{\pi^2}{6} \alpha\sigma\Omega\omega
\int_{x=1}^{n}=\int\limits_{x=1}^{n}
\label{eq:1}
\end{equation}

 We wzorze \ref{eq:1} $x$ oznacza sdfs

 $$\arctan=a^x+y \neq d \le < d \le d > d \ge a^{x+y}\cos{\alpha} \otimes \cos$$

 $$\alpha\neq\gamma\Omega\Gamma\lambda$$

 $$\stackrel {\overline {x} = \frac{x}{2}}{=}$$

 $$\stackrel {\int}{---}$$

 $$\overline{a-b} = \underline{z-o} $$

 $$\underbrace{{\bf a} + b + \cdots + z}$$ %\ wytłuszczanie pojedynczych elementow w trybie math

 $$\underbrace{abc}_{qqq}$$

 $$\overbrace{abc}^{12}$$

 \textbackslash
 ( [ \{ \$ \\

$$\left.\left. \frac{x}{y} \right| ff\right|$$
$$\left. \frac{x}{y} \right| \left.ff\right|$$ %\ z pojedyncza kreska
$$\left. \frac{x}{y} \right| \left.ff\right\|$$ %\ z podwojna kreska

$$\left\Updownarrow \frac{x}{y} \right\}$$

$$\sqrt[\alpha]{x} \sqrt{ s^{2}+\sqrt{y}}$$

%\alpha kappa beta lambda phi

$$ \phi(r) = \frac{e^{-\alpha \left(\frac{r}{r_{e}} -1\right) } A}{\left(\frac{r}{r_{e}} -\kappa\right)^{20} +1} - \frac{e^{-\beta\left(\frac{r}{r_{e}} -1\right) } B}{\left(\frac{r}{r_{e}} -\lambda\right)^{20} +1} $$

\end{document}