It's an infinite geometric series. S = 1/(1-1/4) = 4/3.

Yup! Just to expand, the series is as follows:

$\text{pyramid_size} = \sum_{k=0}^{\infty} \text{image_size} * \frac{1}{4^k}$

$ \quad = \text{image_size} \sum_{k=0}^{\infty} 0.25^k$

$ \quad = \text{image_size} \lim_{k\rightarrow\infty} \left(\frac{1-(0.25)^k}{1-0.25}\right)$

$ \quad = \text{image_size} \left(\frac{1-0}{1-0.25}\right)$

$ \quad = \frac{4}{3} \text{image_size}$