(UPF) A região em cinza do quadrado ABCD se repete infinitamer te, de acordo com o padráo representado na figura originando sempre mais quadrados. square square essa maneira , a fração do quadrado ABC D cará preenchida e (1)/(2) C) (1)/(3) e) 1(1)/(2)

Question

(UPF) A região em cinza do quadrado ABCD se repete infinitamer te, de acordo com o padráo representado na figura originando sempre mais quadrados. square square essa maneira , a fração do quadrado ABC D cará preenchida e (1)/(2) C) (1)/(3) e) 1(1)/(2)

Answer 1

## Step 1: Understanding the Pattern### The image describes a fractal pattern where each square is divided into smaller squares, and some of these are shaded. This pattern repeats infinitely, suggesting a geometric series.## Step 2: Identifying the Shaded Area### The largest inner square (top-left) is shaded, occupying

of the total area of the large square ABCD. The second largest shaded square (bottom-right) also occupies

of the remaining area, which is

of the total area of ABCD. This pattern continues with each subsequent shaded square occupying

of the remaining unshaded area.## Step 3: Calculating the Total Shaded Fraction### The total shaded area forms an infinite geometric series with the first term

and common ratio

. The sum of an infinite geometric series is given by the formula:

Substituting the values, we get:

This means that

of the total area of the square ABCD will be filled with shaded squares as the pattern continues infinitely.

Question

(UPF) A região em cinza do quadrado ABCD se repete infinitamer te, de acordo com o padráo representado na figura originando sempre mais quadrados. square square essa maneira , a fração do quadrado ABC D cará preenchida e (1)/(2) C) (1)/(3) e) 1(1)/(2)

Solution

Resposta

Explicação