Answer:
R must lie between the two values 4 and 7
R ∈ (4,7)
Step-by-step explanation:
∑

converges at x= 0 and Diverges at x= -11
Given series is centered at x= -4
since the series converges at x= 0, which is a distance of 4 from x= -4
=> the radius of convergence (R) is at least 4
since the series diverges at x= -11, which is a distance of 7 from x= -4
=> the radius of convergence (R) cannot be more than 7
=> 4 ≤ R ≤ 9 ⇒ R ∈ (4,7)