Abstract Algebra?

Question

Establish the Bernoulli inequality:

If l+a>0, then (l+a)^n is greater or equal than 1+na for all positive integers n.

Answer 1

Using binomial expansion:
(1+a)^n = 1 + nC1 a + nC2 a^2 + nC3 a^3 + ....
nC1 = n so
(1+a)^n = 1 + na + ....
(1+a)^n ≥ 1 + na

Answer 2

It's an easy inductive proof.

The n=1 step is trivial (both sides of the inequality are the same for n=1).

For the inductive step, multiple both sides of the nth step by 1+a and the (n+1)st step falls right out.