Absolute & conditional convergence - Sequence and Series

Absolute & conditional convergence

In this section, we will learn about the concept of absolute and conditional convergence. We say a series is absolutely convergent if BOTH the series and absolute value of the series is convergent. If the series is convergent and the absolute value of the series is divergent, then we call that conditional convergence. First, we will be use these definitions and apply it to some of the series below. Lastly, we will look at a complicated series which requires us to convert it to a simpler form before showing if it's absolutely convergent, conditionally convergent, or divergent.

Lessons

Notes:

Let $\sum a_n$ be a convergent series. Then we say that $\sum a_n$ is absolutely convergent if $\sum |a_n|$ is convergent.

If $\sum |a_n|$ is divergent, then we say that $\sum a_n$ is conditionally convergent.

1.
Questions based on Absolute & Conditional Convergence
Determine if the series is absolutely convergent, conditionally convergent, or divergent