Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 9 - Infinite Series - 9.5 The Comparison, Ratio, And Root Tests - Exercises Set 9.5 - Page 637: 43

Answer

Diverges

Work Step by Step

Apply the n-th term test. For $a_k \to 0$, the series diverges. Therefore, $ L=\lim\limits_{k \to \infty} \dfrac{1}{4+2^{-k}} \\=\dfrac{1}{4+0}\\=\dfrac{1}{4} \ne 0$ So, we can conclude that the given series diverges by the n-th term test.
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