# Give an example of a series that is conditionally convergent (that is, convergent but not absolutely convergent). Infinite Series, Convergence tests,

\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...

## is convergent by the alternating series test (the terms are alternately positive and negative, and their magnitudes decrease to zero). But

\sum_{n=1}^{\infty}| \frac{(-1)^{n+1}}{n} | =\sum_{n=1}^{\infty}\frac{1}{n}

diverges.