Definition
Bernoulli's Inequality
For every real number
and every natural number , the following inequality holds: If
and , the inequality is strict: .
Proof by Induction
Bernoulli's Inequality
We use induction on
. Base case (
): > . The base case holds. Inductive step:
Assumefor some . We want to show it holds for . Thus, the statement holds for all
by induction.