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: 71

Answer

a) First Four Terms: $0.9 , 0.09, 0.009, 0.0009$ b) $\lim\limits_{n \to \infty} S_n = 1$

Work Step by Step

$$\sum_{k=1}^{\infty} 9(0.1)^k$$ Part A) $a_1 = 9(0.1)^1 = 0.9$ $a_2 = 9(0.1)^2 = 0.09$ $a_3 = 9(0.1)^3 = 0.009$ $a_4 = 9(0.1)^4 = 0.0009$ Part B) $a_1 + a_2 + a_3 + a_4 + ... = 0.9 + 0.09 + 0.009 + 0.0009 + ... = 0.9999...$ The series seems to converge to the value $1$.
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