Question

Look at the figure. What fraction of the square is eventually shaded if the indicated shading process continues indefinitely?

Short answer

The result is one third of the square.

Step-by-step solution

Given information

We are given$a=\frac{1}{4}$

Calculate

We use the formula $S=\frac{a_1}{1-r}$

We have

$$\begin{gathered} S=\frac{{\displaystyle \frac{1}{4}}}{1-{\displaystyle \frac{1}{4}}} \\ S=\frac{1}{3} \end{gathered}$$

Conclusion

The result is one third of the square