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Section 8.8 Absolute Convergence (SQ8)

Subsection 8.8.1 Activities

Activity 8.8.2.

Consider the series βˆ‘n=1∞(βˆ’1)nn2.
(a)
Does the series βˆ‘n=1∞(βˆ’1)nn2 converge or diverge?
(b)
Does the series βˆ‘n=1∞|(βˆ’1)nn2| converge or diverge?

Activity 8.8.7.

For each of the following series, determine if the series is convergent, and if the series is absolutely convergent.
(a)
βˆ‘n=1∞n2(βˆ’1)nn3+1
(c)
βˆ‘n=1∞(βˆ’1)n(23)n

Activity 8.8.8.

If you know a series βˆ‘an is absolutely convergent, what can you conclude about whether or not βˆ‘an is convergent?
  1. We cannot determine if βˆ‘an is convergent.
  2. βˆ‘an is convergent since it β€œgrows slower” than βˆ‘|an| (and falls slower than βˆ‘βˆ’|an|).

Subsection 8.8.2 Videos

Figure 190. Video: Determine if a series converges absolutely or conditionally

Subsection 8.8.3 Exercises