Power series representation

  • #1
I'm trying to do the question attached. I got the first three answers correct knowing that the nth derivative of a function evaluated at 0 divided by n! = c_n. However, I did the same for the others and the answer is incorrect. I know that I need the power series representation of that function in order to get the radius of convergence but I don't know how to get it. Can someone help please?
 

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  • #2
Dick
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Save yourself some labor and work out the power series expansion of log(1+x) first. It has a simple form. Then substitute 2x for x in that and multiply the whole thing by 2x. This is easier and less error prone than taking high order derivatives which get more and more complicated.
 
  • #3
ok thanks but how do I get the terms?
 
  • #4
Dick
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Take higher derivatives again. But this is a much easier function to deal with. Try it.
 

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