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April 17th, 2016, 08:11 PM   #1
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Binomial Series

Consider the binomial function f(x)=sqrt(1+2x).
a) Write f(x) as a binomial series centered at a=0 and determine the radius of convergence.

b) Find Taylor polynomial T3(x) of the series.


I wrote f(x) as (1+2x)^(1/2) and started to write out the series with k=1/2, but I'm not sure where to go from there.

Thank you for your help.
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April 17th, 2016, 08:27 PM   #2
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Could you write the series for (1 + x)^(1/2)? If so, do that, then replace "x" with "2x".
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