Power series representation

1. May 22, 2007

cmantzioros

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. May 22, 2007

Dick

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. May 22, 2007

cmantzioros

ok thanks but how do I get the terms?

4. May 22, 2007

Dick

Take higher derivatives again. But this is a much easier function to deal with. Try it.