University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 9 - Section 9.3 - The Integral Test - Exercises - Page 505: 50



Work Step by Step

Since, we have $\int_n^\infty \dfrac{1}{x^2+4}dx \lt 0.1$ or, $\lim\limits_{a \to \infty} (\dfrac{1}{2} tan^{-1} (a/2) -\dfrac{1}{2} tan^{-1} (n/2))\lt 0.1$ or, $n \gt 2 \tan (\pi/2-0.2) \approx 9.867 $ or, $n \geq 10$ Need to use Recursion mode. we get: $S\approx s_{10}= \Sigma_{n=1}^{10} \dfrac{1}{n^2+4} \approx 0.57$
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