Prove that `(1+x)^ngeq(1+n x),`for all natural number n, where `x >-1.`

Explanation

To prove the inequality \((1+x)^n \geq (1 + nx)\) for all natural numbers \(n\) where \(x \geq -1\), we will use the Principle of Mathematical Induction.

### Step 1: Base Case
We start by proving the base case, \(n = 1\).

For \(n = 1\):
\[
(1+x)^1 = 1 + x
...