\section*{Vorwissen}

\definition \textbf{Geometrische Reihe}
$$
    s_n = a_1 \cdot \frac{1-q^n}{1-q} \qquad \underset{n\to\infty}{\lim} s_n = \frac{a_1}{1-q}
$$
\subtext{Wobei $a_i = a_1 \cdot q^{i-1}$}

\definition \textbf{Binomialkoeffizient}
$$
    \binom{n}{k} := \frac{n!}{k!\cdot(n-k)!}
$$

\method \textbf{Partielle Integration}\\
\subtext{$a<b,\quad f,g:[a,b]\rightarrow\R$ stetig diff.-bar}
$$\int f(x)\cdot g'(x)\ dx = f(x)\cdot g(x) - \int f'(x)\cdot g(x)\ dx$$
$$\int_a^bf(x)g'(x)\ dx = f(b)g(b) - f(a)g(a) -\int_a^b f'(x)g(x)$$

\method \textbf{Substitution}\\
\subtext{$a<b,\quad \phi:[a,b]\rightarrow\R$ stetig diff.-bar,\\ $I \subset \R,\quad \phi([a,b]) \subset I,\quad f: I\rightarrow\R$ stetig}
$$\int_{\phi(a)}^{\phi(b)}f(x)\ dx = \int^b_af(\phi(t))\cdot\phi'(t)\ dt$$
