tricks.tex

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\title{Analyse I - Tricks}
\author{Laura Paraboschi - Simon Lefort}
\date{BA1 - Automne 2023}

\begin{document}

\maketitle

\section{Does it converge?}

From the video by blackpenredpen, \textit{100 series convergence tests}.

\subsection{The fact}
\[\lim_{n \to \infty} \left(1 + \frac{a}{n}\right)^n = e^a\]
\subsection{The list}
\[ \text{As } n \to \infty, \ln(n) \ll n^r \ll b^n \ll n! \ll n^n , \text{ where } p > 0 \text{ and } b > 1 \]
\subsection{The limit}
\[ \lim_{n \to 0} \frac{\sin(n)}{n} = 1\]
\subsection{Best Friend}
\[ \frac{1}{1 - x} = \sum_{n=0}^{\infty} x^n \text{ where } |x| < 1 \]

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