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

Explanation

To prove that \((1+x)^n \geq (1 + nx)\) for all natural numbers \(n\) where \(x \geq -1\), we will use the principle of mathematical induction.

### Step 1: Base Case
First, we check the base case for \(n = 1\).

\[ P(1): (1 + x)^1 \geq 1 + 1 \cdot x \]
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