In the induction proof for $(1+p)^n \geq 1 + np$, a term is dropped and I don't understand why. In What is Mathematics, pg. 15, a proof of 
$(1+p)^n \geq 1 + np$, for $p>-1$ and positive integer $n$
goes as follows:


*

*Substitute $r$ for $n$, then multiply both sides by $1+p$, obtaining:
$(1+p)^{r+1}\geq 1+rp+p+rp^2$

*"Dropping the positive term $rp^2$ only strengthens this inequality, so that
$(1+p)^{r+1}\geq 1+rp+p$, which shows that the inequality will hold for $r+1$."
I don't understand why the $rp^2$ term can be dropped -- if we're trying to prove that the inequality holds, and dropping $rp^2$ strengthens the inequality, then why are we allowed to drop it?
Thanks!

if $a \geq b$ and $b \geq c$, then  $a \geq c $. Since $rp^2$ is positive then it is clear that $x+ rp^2 > x $   
