So my calculus professor has given us this online assignment on power series, and I can't wrap my head around in for the life of me.

Most of the questions are the same, so I think if I get the process down for one of them, then I'll be able to approach the other ones.

ex. The function f(x)= 4xarctan(2x) is represented as a power series:

(see attached image at the bottom, since I'm not sure on how to input that on the computer)

Find the first few coefficients in the power series.

c0=

c1=

c2=

c3=

c4=

Find the radius of convergence R of the series.

Any help would be greatly appreciated!!