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%%  Ein Beispiel der DANTE-Edition
%%  Mathematiksatz mit LaTeX
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%%  Beispiel 10-09-11 auf Seite 233.
%%  Copyright (C) 2018 Herbert Voss
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\begin{document}
\begin{align}
 \sum_{i=1}^{\infty} \frac{1}{i} &= 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}
  +\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}
    +\cdots+\frac{1}{16}+\cdots\\[5pt]
 & \ge 1+\frac{1}{2}+\underbrace{\frac{1}{4}+\frac{1}{4}}_{\frac{1}{2}}
    +\underbrace{\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}}_{\frac{1}{2}}
    +\underbrace{\frac{1}{16}+\cdots+\frac{1}{16}}_{\frac{1}{2}}+\cdots\\[5pt]
 &= 1+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\cdots\to\infty
    \quad\rule{1ex}{1ex}
\end{align}
\end{document}