Question

(1 point) The series ∑Cn(x+4)n converges at x=0 and diverges at x=−11. Based on this information we know something about how big and small the radius of convergence R of the power series can be. Between what two values must R lie?

Answer 1

Answer:

R must lie between the two values 4 and 7

R ∈ (4,7)

Step-by-step explanation:

∑$C_{n}$$(x+4)^{n}$

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)