comparison test
The series
∞∑i=0ai |
with real ai is absolutely convergent if there is a sequence (bn)n∈ℕ with positive real bn such that
∞∑i=0bi |
is and for all sufficiently large k holds |ak|≤bk.
Also, the series ∑ai is divergent if there is a sequence (bn) with positive real bn, so that ∑bi is divergent and ak≥bk for all sufficiently large k.
Title | comparison test![]() |
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Canonical name | ComparisonTest |
Date of creation | 2013-03-22 13:21:48 |
Last modified on | 2013-03-22 13:21:48 |
Owner | mathwizard (128) |
Last modified by | mathwizard (128) |
Numerical id | 4 |
Author | mathwizard (128) |
Entry type | Theorem |
Classification | msc 40A05 |