\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[greek]{babel}
\usepackage{amsmath, amssymb}

\title{1η Εργαστηριακή άσκηση}
\author{Ελένη Άννα Παπαγεωργίου}
\date{Απρίλιος 2025}

\begin{document}

\maketitle

\section{Σύντομη Αναφορά}

\section{Μαθηματικές Εξισώσεις}

\begin{equation}
\pi(n) = \sum_{m=2}^{n} \left[ \sum_{k=1}^{m-1}( \lfloor(m/k)/\lceil m/k \rceil \rfloor \right ) ^{-1} ]
\end{equation}

\begin{equation}
A = \begin{pmatrix}
a_{11} & a_{12} & \ldots & a_{1n} \\
a_{21} & a_{22} & \ldots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m1} & a_{m2} & \ldots & a_{mn}
\end{pmatrix}
\end{equation}

\begin{equation}
\begin{cases}
\alpha = f(z) \\
\beta = f(z^2) \\
\gamma = f(z^3)
\end{cases}
\begin{cases}
x = \alpha^2 - \beta \\
y = 2\gamma
\end{cases}
\end{equation}

\begin{equation}
P_1(n) = \lim_{m\to\infty} \sum_{v=0}^{\infty} (1 - \cos^{2m}(v!^n\pi/n))
\end{equation}

\begin{equation}
\prod_{j>0} \left(\sum_{k\geq 0} a_{jk}z^k\right) = \sum_{n \geq 0} z^n \left(\sum_{\substack{k_0,k_1,\ldots \geq 0 \\ k_0+k_1+\ldots=n}} a_{0k_0}a_{1k_1}\ldots\right)
\end{equation}

\begin{equation}
\sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + x}}}}}}}
\end{equation}

\begin{equation}
\sqrt[3]{i}\sqrt[n+1]{4+5+6+7}
\end{equation}

\begin{equation}
\iint_{0}^{a=n} x \, dx \left(\frac{a+b}{c}\right)^2
\end{equation}

\end{document}
