Limit of the geometric sequence $\{r^n\}$, with $|r| < 1$, is $0$? 
Prove that the $\lim_{n\to \infty} r^n = 0$ for $|r|\lt 1$.

I can't think of a sequence to compare this to that'll work.  L'Hopital's rule doesn't apply.  I know there's some simple way of doing this, but it just isn't coming to me. :(

This is an answer I had earlier posted.
This is not a rigorous proof but helps in visualisation.
If $$-1<x<1$$ and you raise it to any power $n > 1 $ the value of it decreases.
Eg say$ x = 0.1 , x ^2  = 0.01, x^3 = 0.001$ or $x ^n = 0.1 ^ n = \frac{1}{10^n}$ and as $ n$ keeps getting bigger , the denominator approaches $\infty $ and the numerator approaches $0 $
