Find a power series for f'(x) by starting with the convergent geometric series

a) Find a power series for f'(x) by starting with the convergent geometric series

b) Find a power series of f(x) and it's radius of convergence.

Re: Find a power series for f'(x) by starting with the convergent geometric series

Do you understand what the question is asking you to do? You know that (note the "3", not "2", in the numerator. I assume that was a typo). You should also know that a "geometric series" is a series of the form and that the sum of such a series is as long as |r|< 1 so that the series converges.

Now look at . That is not **quite** in the form but can be put in that form. Divide both numerator and denominator by 27 and you get . Now do you see what "a" and "r" must be?

Re: Find a power series for f'(x) by starting with the convergent geometric series

How do we go about finding the radius of convergence?