(New page: == Absolute/Conditional Convergence for Power Series == Does anyone have a good idea what absolute and conditional convergence mean for power series? Absolute convergence is easy enough ...) |
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== Absolute/Conditional Convergence for Power Series == | == Absolute/Conditional Convergence for Power Series == | ||
| − | + | Ok, I've think I've figured out what this means, but if someone can contribute, I would appreciate it. It looks like conditional convergence for power series roughly refers to those endpoints that the ratio test fails to determine. If you use some other test, and find it converges, then it is either absolutely or conditionally convergent. If endpoints that cause it to be a positive (absolute) series, then they are part of the absolutely convergent interval. Only when the endpoint converges and it causes the series to alternate, while its absolute value fails, can you say that it is conditionally convergent. | |
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| + | I know, that was a terrible way to say that. Hopefully you can see what I mean; its easier to show that to describe. | ||
--[[User:Jmason|John Mason]] | --[[User:Jmason|John Mason]] | ||
Revision as of 06:00, 8 November 2008
Absolute/Conditional Convergence for Power Series
Ok, I've think I've figured out what this means, but if someone can contribute, I would appreciate it. It looks like conditional convergence for power series roughly refers to those endpoints that the ratio test fails to determine. If you use some other test, and find it converges, then it is either absolutely or conditionally convergent. If endpoints that cause it to be a positive (absolute) series, then they are part of the absolutely convergent interval. Only when the endpoint converges and it causes the series to alternate, while its absolute value fails, can you say that it is conditionally convergent.
I know, that was a terrible way to say that. Hopefully you can see what I mean; its easier to show that to describe.
