Absolute Convergence

While we first talked about series convergence we in brief mentioned a stronger type of convergence but did not do anything with it as we didn't have any tools at our disposal which we could make use of to work problems involving it.  Now we have some of those tools thus it's now time to talk about absolute convergence in detail.

1^st, let's go back over the definition of absolute convergence.

A series ∑a_n is termed as absolutely convergent if ∑|a_n| is convergent. If ∑a_n is convergent and ∑|a_n| is divergent this known as the series conditionally convergent. We as well have the following fact about absolute convergence.

 

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