009C Sample Midterm 1, Problem 3

Determine whether the following series converges absolutely, conditionally or whether it diverges.

Be sure to justify your answers!

$\sum _{n=1}^{\infty }{\frac {(-1)^{n}}{n}}$

Foundations:
1. A series $\sum a_{n}$ is absolutely convergent if
the series $\sum |a_{n}|$ converges.
2. A series $\sum a_{n}$ is conditionally convergent if
the series $\sum |a_{n}|$ diverges and
the series $\sum a_{n}$ converges.

Solution:

Step 1:

Step 2:

Final Answer:

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