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Proposition: Generalized Triangle Inequality
For all natural numbers $n\ge 1$ and all real numbers (respectively complex numbers) $a_1,\ldots,a_n$ the following inequality holds: $$\left|\sum_{k=1}^n a_k\right|\le\sum_{k=1}^n|a_k|,$$
where $|\cdot|$ denotes the absolute value of real numbers (respectively absolute value of complex numbers).
Table of Contents
Proofs: 1
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References
Bibliography
- Modler, F.; Kreh, M.: "Tutorium Analysis 1 und Lineare Algebra 1", Springer Spektrum, 2018, 4th Edition
