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 Post subject: The radius of convergence and interval of convergencePosted: Wed, 18 Apr 2012 11:53:20 UTC
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How to determine the radius of convergence and interval of convergence for the following power series?

Only jump right into the ratio test?

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 Post subject: Re: The radius of convergence and interval of convergencePosted: Wed, 18 Apr 2012 12:34:38 UTC
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wisheskernel wrote:
How to determine the radius of convergence and interval of convergence for the following power series?

Only jump right into the ratio test?

Over ? Over ?

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 Post subject: Re: The radius of convergence and interval of convergencePosted: Wed, 18 Apr 2012 18:20:10 UTC
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wisheskernel wrote:
How to determine the radius of convergence and interval of convergence for the following power series?

Only jump right into the ratio test?

http://en.wikipedia.org/wiki/Weierstrass_M_test

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"Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another." Bernard Le Bovier Fontenelle (1657-1757)

"In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy."
G.H. Hardy (1877-1947)

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 Post subject: Re: The radius of convergence and interval of convergencePosted: Wed, 18 Apr 2012 21:08:57 UTC
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Justin wrote:
wisheskernel wrote:
How to determine the radius of convergence and interval of convergence for the following power series?

Only jump right into the ratio test?

http://en.wikipedia.org/wiki/Weierstrass_M_test

In sine is not bounded...

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 Post subject: Re: The radius of convergence and interval of convergencePosted: Wed, 18 Apr 2012 22:39:01 UTC
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In sine is not bounded...

I assumed (hopefully correctly) that the OP was referring to .

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"Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another." Bernard Le Bovier Fontenelle (1657-1757)

"In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy."
G.H. Hardy (1877-1947)

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 Post subject: Re: The radius of convergence and interval of convergencePosted: Wed, 18 Apr 2012 23:18:37 UTC
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Justin wrote:

In sine is not bounded, and on this is just dominated convergence.

I assumed (hopefully correctly) that the OP was referring to .

It wasn't clear to me that you meant for the set to be , but yes that works in that case.

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 Post subject: Re: The radius of convergence and interval of convergencePosted: Thu, 19 Apr 2012 08:15:57 UTC
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Joined: Tue, 22 Jan 2008 03:53:38 UTC
Posts: 76
outermeasure wrote:
wisheskernel wrote:
How to determine the radius of convergence and interval of convergence for the following power series?

Only jump right into the ratio test?

Over ? Over ?

Over , How to determine the radius and interval of convergence for the series?

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 Post subject: Re: The radius of convergence and interval of convergencePosted: Thu, 19 Apr 2012 16:14:45 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12170
Location: Austin, TX
wisheskernel wrote:
outermeasure wrote:
wisheskernel wrote:
How to determine the radius of convergence and interval of convergence for the following power series?

Only jump right into the ratio test?

Over ? Over ?

Over , How to determine the radius and interval of convergence for the series?

The M-test is a good choice if you want this as a functional sum. If x is fixed, then you can just use the normal comparison test.

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