## Calculus: Early Transcendentals (2nd Edition)

Published by Pearson

# Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises - Page 604: 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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