Question

Let n be a natural number and each a_0,...,a_n > 0. I'm supposed to prove that
(1+a_0)(1+a_1)...(1+a_n) greater than or equal to 1 + a_1 + a_2 +...+ a_n.
It's in the section where they outline the Triangle Inequality, but I'm not quite sure how to start...

Answer 1

This can be proved by mathematical induction.

Answer 2

That was one way I thought about doing it, but I'm wondering why they stuck it in a section with the Triangle Inequality, Difference of Powers, and Geometric Sum Formula. Thanks!

Answer 3

I'll continue to think about it. Maybe there is a non-inductive way to do it.

Answer 4

Thanks for the help. I appreciate it!