The radius of convergence of a power series ∑ an(x-a)^n is given by:
R = 1/lim sup|an|^(1/n)
To find the interval of convergence, we need to consider two cases:
If R > 0, the series converges for all x within the interval a-R <= x <= a+R.
If R = 0, the series converges only at x = a.
If R = ∞, the series converges for all x.
Therefore, the interval of convergence for the given series is (a-R, a+R).
Note that this is just a general formula for finding the radius of convergence and interval of convergence of a power series. To use this formula, you will need to determine the values of an and a for the specific series you are working with.