I am familiar with the proof for the following variant of the triangle inequality:(adsbygoogle = window.adsbygoogle || []).push({});

|x+y| ≤ |x|+|y|

However, I do not understand the process of proving that there is an equivalent inequality for an arbitrary number of terms, in the following fashion:

|x_1+x_2+...+x_n| ≤ |x_1|+|x_2|+...+|x_n|

How do I prove this? Please write down the solution step by step. I know that the Cauchy-Schwartz inequality is used for proving this in the case where n=2, but is it possible to use it for any n?

Thank you,

Dobedobedo!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof of the triangle inequality

**Physics Forums | Science Articles, Homework Help, Discussion**