If $p \geq 1$ and $a_k, b_k$ are real numbers for $k = 1,\ldots$ , then $$\left( \sum_{k=1}^n |a_k+b_k|^p\right)^{1/p} \le \left(\sum_{k=1}^n |a_k|^p\right)^{1/p} + \left(\sum_{k=1}^n |b_k|^p\right)^{1/p}$$

The Minkowski inequality is in fact valid for all $L^p$ norms with $p\ge1$ on arbitrary measure spaces. This covers the case of listed here as well as spaces of sequences and spaces of functions, and also complex $L^p$ spaces.