Answer: (-b + a, b + a).
Explanation:
To find the radius of convergence of the series, we use the formula:
R = 1/limsup|bn|^(1/n)
To find the interval of convergence, we can use the following:
If R > 0, the series converges for all |x-a| < R and diverges for |x-a| > R.
If R = 0, the series converges only at x = a and diverges for all other values of x.
If R = ∞, the series converges for all values of x.
Therefore, the interval of convergence of the series is (-R + a, R + a).
In this case, the radius of convergence R is given as b, and the interval of convergence is (-b + a, b + a).