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: 61

Answer

First four terms: $4, 0.9, 0.09, 0.009$ Sum: $S = 5$

Work Step by Step

If we ignore the first term, we find that the next term is the previous term multiplied by a factor of $0.1$. Thus, the first four terms are $4, 0.9, 0.09, 0.009$ If we exclude the first term, we find that it's a geometric sequence with the first term $a_0=0.9$ and $r=0.1$, which satisfies $r<1$. $S_\infty = \frac{a_0}{1-r} = \frac{0.9}{0.9} = 1$ To find the total sum, we need to add the first term and $S_\infty$ together: $$S = 4 + S_\infty = 4 + 1 = 5$$
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