How do you do this question?

R = 1

I = [-1, 1)

Step-by-step explanation:

Use the ratio test:

lim(n→∞)│aₙ₊₁ / aₙ│

lim(n→∞)│[xⁿ⁺¹ / (8(n+1) − 1)] / [xⁿ / (8n − 1)]│

lim(n→∞)│[xⁿ⁺¹ / (8n + 7)] × [(8n − 1) / xⁿ]│

lim(n→∞)│[x (8n − 1) / (8n + 7)]│

lim(n→∞)│[(8n − 1) / (8n + 7)]││x│

│x│

The series converges if the limit is less than 1.

│x│< 1

So the radius of convergence is 1.

Solving for x:

-1 < x < 1

Check the endpoints.

If x = -1, the series is ∑ (-1)ⁿ / (8n − 1), which converges.

If x = 1, the series is ∑ 1 / (8n − 1), which diverges.

So the interval of convergence is [-1, 1).

yes

step-by-step explanation: