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November 13th, 2012, 01:52 PM  #1 
Newbie Joined: Oct 2012 Posts: 10 Thanks: 0  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? 
November 13th, 2012, 04:58 PM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  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. 
November 13th, 2012, 08:24 PM  #3 
Newbie Joined: Oct 2012 Posts: 10 Thanks: 0  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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binomial, power, series, theorem, write 
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