- #1
I need to proof convergence, and find the radius of converge
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- Convergence Proof Radius
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Homework Help Overview
The discussion revolves around proving convergence of a series and finding its radius of convergence. The participants are exploring the properties of series and applying convergence tests in the context of sequences.
Discussion Character
- Exploratory, Assumption checking, Mathematical reasoning
Approaches and Questions Raised
- Participants discuss the comparison test and its application to the series in question. There are attempts to justify choices of variables and limits, with some questioning the reasoning behind convergence assumptions. The structure of the series is also analyzed, particularly in relation to its form as a power series.
Discussion Status
The discussion is active, with participants providing hints and questioning each other's reasoning. Some guidance has been offered regarding the use of the comparison test, but there is no explicit consensus on the conclusions drawn so far.
Contextual Notes
There are indications of missing information regarding the specific series being analyzed, and participants are encouraged to justify their reasoning more thoroughly. The discussion reflects a learning environment where assumptions are being scrutinized.
- #2
Dick
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For the first one, you are given the first series converges. That means a_n->infinity. Think comparison test. 1/(a_n-x)<1/(a_n-y) if x<y<a_n. How about choosing y=a_n/2?? Can you justify that? For the second one, write it as [(n+1)^n/n^n]*[1/n^z]. The first factor has a limit. What is it?
- #3
asi123
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Dick said:
Right, it's e. so that's mean that in order for the series to converge, x need to bigger then 1?
- #4
Dick
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Looks to me like aside from the e, it's a power series.
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- #6
Dick
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asi123 said:
Why do you think 1/(a_n-2) converges? Shouldn't you state a reason?
- #7
asi123
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Dick said:
If 1/(a_n-2) converges, than why shouldn't 1/(a_n-2) converge? I mean if a_n -> infinity than I don't think that 2 will bother him, no?
- #8
Dick
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asi123 said:
No, the 2 won't bother him. But you still have to show that. Set up a comparison test with something you know converges. Review my hint about this one.
- #9
asi123
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Dick said:
Yeah, I got you, thanks.
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