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: 42

Answer

Converges. The limit of the sequence seems to be $\pi$.

Work Step by Step

$a_n = 2tan^{-1}(1000n)$ $a_1 = 3.13959$ $a_2 = 3.14059$ $a_3 = 3.14093$ $a_4 = 3.14109$ $a_5 = 3.14119$ $a_6 = 3.14126$ $a_7 = 3.14131$ $a_8 = 3.14134$ $a_9 = 3.14137$ $a_{10} = 3.14139$ Converges; the sequence seems to get closer to $\pi$ as $n$ increases.
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