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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).

| | | | | created: 2020-06-26 16:36:43 | modified: 2020-06-26 16:40:29 | by: bookofproofs | references: [8311]

1.Proof: (related to "Generalized Triangle Inequality")

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Bibliography (further reading)

[8311] Modler, F.; Kreh, M.: “Tutorium Analysis 1 und Lineare Algebra 1”, Springer Spektrum, 2018, 4. Auflage