[PS] More detailed descriptions

semester4/ps/ps-jh/parts/10_tips-and-tricks/01_various.tex

@@ -53,5 +53,13 @@ $\cosh(x) := \frac{\sinh(x)}{\cosh(x)} = \frac{e^x - e^{-x}}{e^x + e^{-x}} : \R
 
 
 \subsubsection{Reihen}
-\label{sec:series}
 $\prod_{k = 1}^{n} \vartheta (1 - \vartheta)^{x_k - 1} = \vartheta^n (1 - \vartheta)^{S - n}$ mit $S = \sum_{k = 1}^{n} x_k$
+
+$\sum_{k = 1}^n k = \frac{n \cdot (n + 1)}{2}$; $\sum_{k = 1}^{n} k^2 = \frac{n \cdot (n + 1) \cdot (2n + 1)}{6}$;
+
+$\sum_{k = 1}^{n} k^3 = \left( \frac{n \cdot (n + 1)}{2} \right)^2$;
+$\sum_{k = 1}^{n} \frac{1}{k^2} = \frac{\pi^2}{6}$
+
+Arithmetic series: $s_n = \frac{n \cdot (2a_1 + (n - 1) \cdot d)}{2}$, mit $d$ Differenz
+
+Geometric series: $s_n = a_1 \frac{1 - q^n}{1 - q}$, mit $q$ Quotient