Answer:
R = ∞
I = (-∞, ∞)
Step-by-step explanation:
Use the ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│
lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] / [xⁿ⁺⁵ / (2n!]│
lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] × (2n! / xⁿ⁺⁵)│
lim(n→∞)│x 2n! / (2(n+1)!)│
lim(n→∞)│n! / (n+1)!││x│
lim(n→∞) (1 / (n+1))│x│
0
The series converges if the limit is less than 1.
The limit is always less than 1, so the radius of convergence is infinite.
So the interval of convergence is (-∞, ∞).
