Question

How would you find the radius of convergence when you end up with something like |8x - 1| < 1? Do I divide everything by 8 and get a radius of 1/8?

Answer 1

|8x-1| < 1
-1 < 8x-1 < 1
0 < 8x < 2
0 < x < 1/4

Answer 2

Would the radius be 1/4 then?

Answer 3

I look at it this way:
|8x - 1| < 1

8x-1 < 1 AND -(8x - 1) < 1
8x < 2 AND -8x < 0
x < 1/4 AND x > 0

0 < x < 1/4 , the same as Steve's answer.