Absolute Convergence

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This video was originally a part of a larger video lecture, so please pardon any out of place references to example problems, etc. that came from these videos' original contexts.
The original lecture this video came from can be found here:
• The Alternating Series...
The full playlist of these Calculus theory videos can be found here:
• Calculus 2 Theory
You can find a playlist of all my Calculus lectures (where these theory videos were originally a part) here:
• Calculus 2 Lectures

[@User-fe2lb]

Sir why is there no Absolute Divergent

[@SerpentineIntegral]

Well, the short answer is: it's just terminology, and apparently no one has wanted to define such a term yet. But maybe we can see why: If "absolutely convergent" means the series converges when you replace all the terms with their positive versions, then presumably "absolutely divergent" would mean the series DIVERGES when you replace all its terms with their positive versions. But that's the same as saying "the series is NOT absolutely convergent", so why invent a new word just for that? However, another possible meaning for "absolutely divergent" might be "the series diverges whether or not you make its terms positive". But this is also kind of a useless thing to say, because if a series diverges, then its positive-term version is GUARANTEED to diverge also, so there's no reason to make such a distinction.

[@User-fe2lb]

@@SerpentineIntegral thank you sir for the explanation 😊