University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.4 - Comparison Tests - Exercises - Page 509: 12

Answer

Converges

Work Step by Step

Consider $a_n=\dfrac{2^n}{3+4^n}$ and $b_n=\dfrac{ 1}{2^n}$ Now, $\lim\limits_{n \to \infty}\dfrac{a_n}{b_n} =\lim\limits_{n \to \infty}\dfrac{\dfrac{2^n}{3+4^n}}{\dfrac{ 1}{2^n}}$ Thus, we have $ =\lim\limits_{n \to \infty} \dfrac{4^n}{3+4^n}$ or, $=1$ Hence, the series is a convergent series due to the limit comparison test.
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