Bernoulli's Inequality/Corollary/Proof 1

Proof
Let $0 < x < 1$.

Let $y = -x$.

Then $y > -1$ and by Bernoulli's Inequality:


 * $\paren {1 + y}^n \ge 1 + n y$

Thus:
 * $\paren {1 + \paren {-x} }^n \ge 1 + n \paren {-x}$

Hence the result.