<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\nopagenumbers
\hsize = 6in
\vsize = 1.5in
$$
\begin_layout Paragraph*
Induktionsschluss
\end_layout

\begin_layout Standard
Zu zeigen ist 
\begin_inset Formula $\sum_{k=1}^{n+1}k=\frac{(n+1)(n+2)}{2}$
\end_inset

:
\end_layout

\begin_layout Standard
\begin_inset Formula \[
\sum_{k=1}^{n}k=(\sum_{k=1}^{n}k)+(n+1)=^{A(n)}\frac{n(n+1)}{2}+(n+1)=(n+1)(\frac{n}{2}+1)=\frac{(n+1)(n+2)}{2}\Rightarrow A(n+1)\]

\end_inset


\end_layout

\begin_layout Standard
Daraus folgt 
\begin_inset Formula $A(n)$
\end_inset

 ist richtig 
\begin_inset Formula $\forall n\in N$
\end_inset

.
\end_layout
$$
\end
</pre></body></html>