How do I prove the circumference of the Koch snowflake is divergent? How do I prove that the circumference of the Koch snowflake is divergent?

Let's say that the line in the first picture has a lenght of $3cm$.
Since the middle part ($1cm$) gets replaced with a triangle with sidelenghts of $1cm$ each 
we can assume that the circumference increases by the $\frac{4}{3}$-fold.
I guess to calculate the circumference the following term should work, no?
$\lim\limits_{n \rightarrow \infty}{3cm\cdot\frac{4}{3}^n}$
I know that the limit of the circumference is divergent ( $+\infty$).
I also know that a divergent sequence is defined as :

But how do I prove syntactically and mathematically correct that the sequence diverges to $+\infty$ ?

Hint:$$\frac{4^n}{3^n}=L\quad\Rightarrow\quad n=\log_{4/3}L$$
