examday

/TMUA

The curves $C_n$ are defined by $|x|+|y|=2^{2-n}$ for non-negative integers $n$. The region between $C_n$ and $C_{n+1}$ is shaded when $n$ is even, and unshaded when $n$ is odd, as shown in the diagram. This pattern continues infinitely.

Find the total shaded area.