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.
Let ∑an be a convergent series. Then we say that ∑an is absolutely convergent if ∑∣an∣ is convergent.
If ∑∣an∣ is divergent, then we say that ∑an is conditionally convergent.
Questions based on Absolute & Conditional Convergence
Determine if the series is absolutely convergent, conditionally convergent, or divergent
Absolute & conditional convergence
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