Answer
$$\sum\limits_{n = 1}^5 {\frac{1}{n}} {\left( { - 1} \right)^{n + 1}}$$
Work Step by Step
$$\eqalign{
& 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} \cr
& {\text{We can write the series as:}} \cr
& \frac{1}{1} + \frac{1}{2}\left( { - 1} \right) + \frac{1}{3} + \frac{1}{4}\left( { - 1} \right) + \frac{1}{5} \cr
& {\text{Then }} \cr
& {a_n} = \frac{1}{n} \cr
& {\text{The sign of the terms are alternating, then we must add }}{\left( { - 1} \right)^n} \cr
& \sum\limits_{n = 1}^5 {\frac{1}{n}} {\left( { - 1} \right)^{n + 1}} \cr} $$
