We need to prove this with mathematical induction;

$\displaystyle

(1+x)^r \geq 1 + rx

$

r is natural number and $\displaystyle x \geq -1$

So if I insert r = 1 and x = -1

I get $\displaystyle 0 \geq 0$

so it's true.

Then I insert r + 1, and I get

$\displaystyle (1+x)^{r+1} \geq 1 + x(r + 1)$

$\displaystyle (1+x)^{r+1} \geq 1 + xr + x$

What now? I just insert a value for x?