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]

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