Lecture - Analysis MT22, II
Flashcards
What is Bernoulli’s inequality about $x \in \mathbb{R}$, $x > -1$ and $n \in \mathbb{N}$?
\[(1 + x)^n \ge 1 + nx\]
How can you prove Bernoulli’s inequality $(1 + x)^n \ge 1 + nx$?
Via induction on $n$.
What is the triangle law about reals $a, b$?
\[\vert a + b \vert \le \vert a \vert + \vert b \vert\]
What is the reverse triangle law about reals $a, b$?
\[\vert \vert a \vert - \vert b \vert \vert \le \vert a - b \vert\]