Algebra 2 (1st Edition)

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

Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Skill Practice - Page 815: 51


$S_6=\dfrac{1365}{256} \approx 5.332$

Work Step by Step

Here, we have $\sum_{i=1}^6 4(1/4)^{i-1}$ We know that $S_{n}=a_1(\dfrac{1-r^{n}}{1-r})$ Now, $S_6=4[\dfrac{1-(1/4)^{6}}{1-(1/4)}]$ or, $=4 \times (\dfrac{4096/4096-1/4096}{3/4})$ or, $=4 \times \dfrac{1365}{1024}$ Hence, $S_6=\dfrac{1365}{256} \approx 5.332$
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