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Chapter 12: Q. 88 (page 825)

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

Short Answer

Expert verified

The result is one third of the square.

Step by step solution

01

Given information

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

02

Calculate

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

We have

$S = \frac{\frac{1}{4}}{1 - \frac{1}{4}} S = \frac{1}{3}$

03

Conclusion

The result is one third of the square

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Most popular questions from this chapter

In Problems 71-82, find the sum of each sequence.

$\sum_{k = 1}^{40} k$

If $$ 1000$ is invested at $4 %$ per annum compounded semiannually, how much is in the account after 2 years?

In Problems 51–66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

$8 + 4 + 2 + . . . .$

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.

$1, \frac{1}{2}, 3, \frac{1}{4}, 5, \frac{1}{6}, 7, \frac{1}{8}, . . .$

In Problems 71-82, find the sum of each sequence.

${\sum k^{3}}_{k = 4}^{24}$

See all solutions

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