TeX Quellcode:

\begin{array}{rcl}\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\left(1-\dfrac{1}{16}\right)\left(1-\dfrac{1}{25}\right)\dots\left(1-\dfrac{1}{100}\right) &=& \left(1-\dfrac{1}{2}\right)\left(1+\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)\left(1+\dfrac{1}{4}\right)\left(1-\dfrac{1}{5}\right)\left(1+\dfrac{1}{5}\right)\dots\left(1-\dfrac{1}{10}\right)\left(1+\dfrac{1}{10}\right) \cr\cr&=& \dfrac{1}{2}\cdot\;\dfrac{3}{2}\cdot\dfrac{2}{3}\;\cdot\;\dfrac{4}{3}\cdot\dfrac{3}{4}\;\cdot\;\dfrac{5}{4}\cdot\dfrac{4}{5}\;\cdot\;\dfrac{6}{5}\cdot\;\dots\;\cdot\dfrac{9}{10}\cdot\;\dfrac{11}{10} \cr\cr&=& \dfrac{1}{2}\cdot 1\cdot 1\cdot 1\cdot\;\dots\;\cdot\dfrac{11}{10} \cr\cr&=& \dfrac{11}{20}\end{array}