# Lecture - Analysis MT22, Lecture 2

> Source: https://ollybritton.com/notes/uni/prelims/mt22/analysis-i/lectures/2/ · Updated: 2022-10-20 · Tags: uni, lecture

- [Course - Analysis MT22](https://ollybritton.com/notes/uni/prelims/mt22/analysis-i/)

### 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 $a, b$?::
$$
|a + b| \le |a| + |b|
$$

What is the reverse triangle law about reals $a, b$?::
$$
||a| - |b|| \le |a - b|
$$

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