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: 8

Answer

$\frac{25}{12}$

Work Step by Step

$$\sum_{k=1}^{\infty} \frac{1}{k}$$ To find the partial sum of the first four terms, we need to find the values when $k=1$, $k=2$, $k=3$, and $k=4$ and add them together. $$\sum_{k=1}^{4} \frac{1}{k} = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{25}{12}$$
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