To the first question: Recall that the power series expansion for is the series (this is derived by taking the derivative of the well know power series for )

So we have that:

therefore, we have

use that to find the first few coefficients

For the second question:

use the root test (or if you prefer, the ratio test, either one works nicely in this case) to find the radius of convergence. do you need help with that part?