I am supposed to find the limits as $n\rightarrow\infty$ of the perimeter & area of a snow flake.
$$N_n = \text{Number of sides} = 3\cdot 4^n$$
$$L_n = \text{length of side} = \frac{1}{3^n}$$
$$l_n = \text{perimeter} =N_n \cdot L_n = 3(\frac{4}{3})^{n} $$
$$l_n = 4 (\frac{4}{3})^{n-1}$$
$$\lim_{n\to\infty} l_n = \lim_{n\to\infty} 4 (\frac{4}{3})^{n-1} = \infty$$
Is this correct?
For area, the link has the answer, but I don't understand why is the area given by
$$A_n = A_{n-1} + \frac{1}{4} N_n L_{n}^2 A_0$$