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: 51

Answer

$n \gt 10^{60}$

Work Step by Step

Since, we have $\int_n^\infty \dfrac{1}{x^{1.1}}dx \lt 0.00001$ or,$ \lim\limits_{a \to \infty} (\dfrac{-10}{a^{0.1}}+\dfrac{10}{n^{0.1}})\lt 0.00001$ or, $\dfrac{10}{n^{0.1}} \lt 0.00001 $ or, $n \gt (10^6)^{10}$ Hence, $n \gt 10^{60}$
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