Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Section 10.6 - Alternating Series and Conditional Convergence - Exercises 10.6 - Page 603: 33


Absolutely converges

Work Step by Step

Let us consider the Ratio Test of the given series. In order to solve this series , we have: $\lim\limits_{n \to \infty} |\dfrac{u_{n+1}}{u_n}|=\lim\limits_{n \to \infty} |\dfrac{u_n \times \dfrac{-100}{(n+1)}}{u_n}\\=\lim\limits_{n \to \infty} \dfrac{100}{(n+1)}\\=0 \lt 1$ This implies that the series Absolutely converges by the ratio test.
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