- #1

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[tex]\left| a + b \right| \le \left| a \right| + \left| b \right|[/tex]

I was reading a source which asserted the following extension of the triangle inequality:

[tex]\left| a + b \right|^p \le 2^p \left(\left| a \right|^p + \left| b \right|^p\right)[/tex]

This is bugging me because I can't figure out how to prove or disprove it. It's sensible enough that it might actually be true... but want to know for sure whether it's true.

I tried proving it by induction, but it got really messy...

Is this inequality true? Or, is it wrong? Thanks!