Absolutely Convergent
Definition
When a series ∑a_n is absolutely convergent, it means that the sum of the absolute values of its terms, ∑|a_n|, converges. In other words, the positive version of the series converges.
Analogy
Imagine you have a jar filled with both positive and negative marbles. If you take out all the marbles and count only the number of marbles without considering their signs (i.e., their absolute values), and this count is finite, then we can say that the sum of all marbles converges.
Related terms
Conditional Convergence: A series that converges but not absolutely.
Divergence: A series that does not converge.
Alternating Series Test: A test used to determine if an alternating series converges or diverges based on certain conditions.
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