Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 9 - Inifnite Series - 9.1 Exercises - Page 592: 42

Answer

converges to $0$

Work Step by Step

To determine whether a sequence converges, determine if the limit as $n$ approaches infinity is a constant. To make the limit easier, change the $-3^{-n}$ into $-\frac {1}{3^{n}}$ using exponent rules and then take the limit. $\lim\limits_{n \to \infty} -3^{n}=\lim\limits_{n \to \infty} -\frac {1}{3^{n}}=0$ Therefore, the sequence converges to 0.
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