Apologies for the (maybe obvious) question. It's come up as part of a proof of the triangle inequality for a metric function I'd like to work with.
For real number $r \geq 1$ and positive integers a, b, c:
Is it generally true that $r^a \leq r^b+r^c$? Given that $a \leq b + c$.
Happy to accept a pointer in the right direction.