Answer
The answer is $\frac{1}{3}$.
Work Step by Step
First shaded part $=\frac{1}{4}$.
Second shaded part $=\frac{1}{16}$.
Third shaded part $=\frac{1}{64}$ and so on.
This is the geometric sequence series.
$\frac{1}{4},\frac{1}{16},\frac{1}{64},...$ infinite times.
common ratio $=\frac{1}{4}$.
The total part shaded of the largest square is.
$=\frac{\frac{1}{4}}{1-\frac{1}{4}}$
$=\frac{\frac{1}{4}}{\frac{4-1}{4}}$
$=\frac{\frac{1}{4}}{\frac{3}{4}}$
$=\frac{1}{3}$.
