Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Section 10.2 - Infinite Series - Exercises 10.2 - Page 580: 63



Work Step by Step

Formula to calculate the sum of a geometric series is: $S=\dfrac{a}{1-r}$; Since, we have two series $\sum_{n =1}^{ \infty}\dfrac{2^n+3^n}{4^n}=\sum_{n =1}^{ \infty} (\dfrac{1}{2})^n+\sum_{n =0}^{ \infty} (\dfrac{3}{4})^n$ Here, $a=\dfrac{1}{2},\dfrac{3}{4}$ and common ratios are: $r =\dfrac{1}{2},\dfrac{3}{4}$ Now, Thus, $S=s_1+s_2=\dfrac{1/2}{1-\dfrac{1}{2}}+\dfrac{3/4}{1-\dfrac{3}{4}}$ or, $=1+3$ or, $=4$
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