Difference between revisions of "Comparison test for real series"
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Latest revision as of 07:28, 23 November 2016
Stub grade: A*
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Flesh out, link, then demote. This is needed for functional analysis
Contents
[hide]Statement
Suppose (an)n∈N and (bn)n∈N are real sequences and that we have:
- ∀n∈N[an≥0∧bn≥0] - neither sequence is non-negative, and
- ∃K∈N∀n∈N[n>K⟹bn≥an] - i.e. that eventually bn≥an.
Then:
Proof
Case 1
- Uses A monotonically increasing sequence bounded above converges, my notes in the picture are VERY messy but get there in the end.
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Case 2
Grade: C
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Routine, but would be good to do
References
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Please note that this does not mean the content is unreliable, it just means that the author of the page doesn't have a book to hand, or remember the book to find it, which would have been a suitable reference.
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See correspondence with David Guichard on 22/11/2016 for where I sourced this
Categories:
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- Theorems
- Theorems, lemmas and corollaries
- Real Analysis Theorems
- Real Analysis Theorems, lemmas and corollaries
- Real Analysis
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- Functional Analysis