Hey guys, im not quite getting how to solve by induction for inequalities. An example of the work i have to do is as follows:

Suppose that a and b are real numbers with 0 < b < a.

Prove that if n is a positive integer, then

$\displaystyle

a^n - b^n \leq na^{n-1}(a-b)

$

Thanks a bunch in advance guys!