8
$\begingroup$

The question reads

$$U_n = (1+x)^n - 1 - nx$$ Show that $U_2 \geq 0$ Hence or otherwise show that $(1+x)^n \geq 1 + nx$ for all $x \gt -1$.

Obviously the $U_2 \geq 0$ is very easy, I can do that without any trouble but I cannot see how it links to the 2nd part of the question.

4 Answers 4