exercise:C3f265f368: Difference between revisions
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As a corollary of | As a corollary of [[guide:6d9eb91468#theorem-1|theorem]], prove the following extension of the Comparison Test: | ||
extension of the Comparison Test: | |||
The series <math>\sum_{i=m}^\infty a_i</math> is absolutely convergent if there exists an absolutely convergent series <math>\sum_{i=m}^\infty b_i</math> such that <math>|a_i| \leq |b_i|</math> eventually. | |||
is absolutely convergent if there exists an | |||
absolutely convergent series <math>\sum_{i=m}^\infty b_i</math> | |||
such that <math>|a_i| \leq |b_i|</math> eventually. | |||
Latest revision as of 03:16, 25 November 2024
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[/math]
As a corollary of theorem, prove the following extension of the Comparison Test:
The series [math]\sum_{i=m}^\infty a_i[/math] is absolutely convergent if there exists an absolutely convergent series [math]\sum_{i=m}^\infty b_i[/math] such that [math]|a_i| \leq |b_i|[/math] eventually.