True-False Quiz Question 12: A Divergent Series is Also Absolutely Divergent

In this video I show that a divergent series also means that the absolute value of the series is divergent. This follows from my earlier theorem that an absolutely convergent series is also convergent. Thus if the opposite were true, a divergent series would mean that it would be absolutely convergent, and hence convergent, which is a contradiction! Thus, the answer to the question is True, and a divergent series is also absolutely divergent.

Note that I made a typo in the video, the absolute value sign should be inside the summation series. Nonetheless, I solved it as if was inside.

Time stamps:

• Question 12: 0:00
• Solution: True: 0:13
• Theorem: An absolutely convergent series is also convergent: 1:44

Full video below:

• Infinite Sequences and Series: Review and True-False Quiz:
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