adjective
Convergent is an adjective that describes something that comes together or meets at a point.
adverb
Convergent can also be used as an adverb to describe the manner in which something is coming together.
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The series is absolutely convergent, meaning it converges regardless of the order of terms.
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The sum is absolutely convergent, so it doesn't matter how you add up the numbers.
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This sequence is totally convergent, no matter what.
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Her dedication to her work is like an absolutely convergent series, unwavering and constant.