Bernoulli's Inequality/Corollary/Proof 1

Proof
Let $0 < x < 1$.

Let $y = -x$.

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


 * $\left({1 + y}\right)^n \ge 1 + n y$

Thus:
 * $\left({1 + \left({-x}\right)}\right)^n \ge 1 + n \left({-x}\right)$

Hence the result.