Why is this inequality important? $(1+p)^n\geq 1+np$ I'm reading Courant's What is Mathematics?
In the beginning, he's showing some proofs, there's a proof about An Important Equality and this important equality is:
$$(1+p)^n\geq 1+np$$
The book's author states the proof but he doesn't say why the inequality is important, I had a feeling that this inequality importance is by stabilishing the $\geq$ relation in $\mathbb{N}$, is this it's importance? If not, what is it?

It is usually called Bernoulli's inequality. It frequently appears in mathematical contests. This inequality is important, because many other inequalities can be proved using it. Here is some person's Bachelor's thesis where it is mentioned among others; in particular, reference [60; Zhu H.] seems to offer some explanation with applications, but I could not find an on-line version.
