Category:Properly Divergent Series
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This category contains results about Properly Divergent Series.
Definitions specific to this category can be found in Definitions/Properly Divergent Series.
Let $s$ be an infinite series:
- $s = \ds \sum_{k \mathop = 1}^\infty a_k = a_1 + a_2 + a_3 + \cdots$
Then $s$ is a properly divergent series if and only if it is a divergent series such that either:
- $s_n \to \infty$ as $n \to \infty$
or:
- $s_n \to -\infty$ as $n \to \infty$
where $s_n$ is the $n$th partial sum of $s$:
- $s_n = \ds \sum_{k \mathop = 1}^n a_k$
Subcategories
This category has only the following subcategory.