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November 13th, 2012, 01:52 PM   #1
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Using the Binomial Theorem to write a power series

Hello!

Using the Binomial Theorem write [attachment=1:3ibjj3gt]gif.latex.gif[/attachment:3ibjj3gt] as a power series.

I got

[attachment=0:3ibjj3gt]gif.latex1.gif[/attachment:3ibjj3gt]

Is this correct? And how can i find the radius of convergence for this?
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File Type: gif gif.latex1.gif (1.2 KB, 162 views)
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November 13th, 2012, 04:58 PM   #2
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Re: Using the Binomial Theorem to write a power series

I haven't done the detailed calculations but it certainly looks correct. And to find the radius of convergence use the "ratio test".

In order that the sequence converge, the limit of that must be less than 1. Find the limit, set it less than 1, and determine what x must be.
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November 13th, 2012, 08:24 PM   #3
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Re: Using the Binomial Theorem to write a power series

Thank you very much!
I have one more question.
How can I use the results from this to find a power series representation for

[attachment=0:1gz724ny]gif.latex.gif[/attachment:1gz724ny]
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