Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.3 - Geoetric Sequences and Series - Exercise Set - Page 1076: 87



Work Step by Step

The shaded areas form a geometric series: $(0.5a)^2, ((0.5)^2a)^2, ((0.5)^3a)^2 ,...$ where $a$ is the side length of the largest square. We, have $a_1=(0.5)^2a^2, r= (0.5)^2$ Thus, the sum of all the areas is $S=\frac{a_1}{1-r}=\frac{(0.5)^2a^2}{1-(0.5)^2}=\frac{1}{3}a^2$ and the ratio is $\frac{S}{a^2}=\frac{1}{3}$
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