Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 3


As $n$ increases $S_n$ also increases, and the value approaches $0.75$ as $n \to \infty$ .

Work Step by Step

Here we have $S_1=\dfrac{1}{2}=0.5; \\S_2=\dfrac{1}{2}+\dfrac{1}{6}=0.67 ; \\S_3=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}=0.72 ; \\S_4=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}=0.74 ; \\ S_5=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{162}=0.75$. Thus, as $n$ increases $S_n$ also increases and the value approaches $0.75$ as $n \to \infty$
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