Question 120
A television screen measures $60\ \mathrm{cm}\times45\ \mathrm{cm}$. A camera frames the whole television and sends the image back to its own screen, so another television appears inside it, and so on. The largest television visible inside the screen has half the screen's area. Suppose a viewer sits at a distance where images smaller than $1\ \mathrm{cm}^2$ cannot be distinguished. How many televisions does the viewer see inside the screen?