(UPF) A região em cinza do quadrado ABCD se repete infinitament e, de acordo com o padrão representa do na figura ,originando sempre mais quadrados. square square square square Dessa maneira, a fração do quadrado A BCD que ficará preenchid e a) (1)/(2) C) (1)/(3) e) 1(1)/(2)

## Step 1: Understanding the Pattern### The large square ABCD is divided into smaller squares, with a fractal-like pattern where grey and white squares alternate. The pattern repeats infinitely, creating more squares within each iteration.## Step 2: Calculating the Fraction of Grey Area### To determine the fraction of the square that will be shaded grey, we need to analyze the pattern's repetition and how much area each iteration adds to the grey region.### Initially, the bottom-left quarter of the square is grey. In each subsequent iteration, smaller grey squares are added in a similar pattern.## Step 3: Summing the Series### The initial grey area is of the total area. Each subsequent iteration adds grey squares that are of the remaining white area from the previous iteration.### This forms an infinite geometric series where the first term and the common ratio . ### Substituting the values: ## Step 4: Conclusion### Therefore, the fraction of the square ABCD that will be filled with grey squares is .