1. (UPF) A região em cinza do quadrado ABCD se repete infinitame nte, de acordo com o padrãc representa do na figura ,originando sempre mai quadrados. square square square square Dessa maneira, a fração do quadrado AB CD ficará preenchida e a) (1)/(2) C) (1)/(3) e) 1(1)/(2) b) (1)/(4) d) (5)/(4)

## Step 1: Understanding the Recursive Pattern### The image describes a recursive pattern within a square, where each quadrant is further divided into smaller squares. This pattern continues infinitely, suggesting a fractal-like structure.## Step 2: Analyzing the Shaded Area### The shaded area represents the part of the square that is filled as the pattern repeats. Since the pattern is recursive and infinite, we need to determine the fraction of the entire square that will be filled by these shaded areas.## Step 3: Calculating the Fraction Filled### In such recursive patterns, especially when they are infinite, the total area filled can often be calculated using geometric series. If each iteration fills a certain fraction of the remaining space, the sum of these fractions can converge to a specific value.## Step 4: Applying Geometric Series### Let's assume the first iteration fills of the square (as it divides into four quadrants). Each subsequent iteration fills a fraction of the remaining unfilled space. The series for the filled area would be: ### This is an infinite geometric series with the first term and common ratio . The sum of an infinite geometric series is given by: ## Step 5: Conclusion### Therefore, the fraction of the square ABCD that will be filled by the shaded regions as the pattern repeats infinitely is .