Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises: 41

Answer

The sequence converges to $0$.

Work Step by Step

$a_n = cot^{-1}(2^n)$ $a_1 = 0.463638$ $a_2 = 0.244979$ $a_3 = 0.124355$ $a_4 = 0.0624188$ $a_5 = 0.0312398$ $a_6 = 0.0156237$ $a_7 = 0.00781234$ $a_8 = 0.00390623$ $a_9 = 0.00195312$ $a_{10} = 0.000976562$ The sequence seems to approach $0$ as $n$ increases.
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