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Results tagged with limits-and-convergence
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user 6316
Convergence of series, sequences and functions and different modes of convergence.
45
votes
5
answers
3k
views
How many rearrangements must fail to alter the value of a sum before you conclude that none do?
This will not be altogether unrelated to this earlier question.
For which classes $C$ of bijections from $\{1,2,3,\ldots\}$ to itself is it the case that for all sequences $\{a_i\}_{i=1}^\infty$ of r …
30
votes
1
answer
1k
views
Rearrangements that never change the value of a sum
I posted this question on math.stackexchange.com and so far the only answer posted (also mentioned in the comments under the question) shows that one of my rash initial guesses about the bottom-line a …
2
votes
0
answers
153
views
More on rearrangements of series . . .
Earlier I posted this question. First I'll quote the question before refining it and elaborating on it:
For which classes $C$ of bijections from $\{1,2,3,\ldots\}$ to itself is it the case that fo …
2
votes
1
answer
302
views
Division methods for divergent continued fractions
I hadn't even noticed before entering the subject above the parallel with the title of an earlier question posted here titled Summation methods for divergent series. And it's just mutatis mutandis as …
1
vote
0
answers
231
views
Conditional convergence and rearrangements
Is the concept of conditional convergence of series whose terms are real numbers a topic of research in analysis or merely something to be aware of?
The question is prompted by the conjunction of my …