Question

I'm having trouble figuring out the radius of convergence for a power series. I'm applying both the root and ratio tests and coming up with different answers, and I'm sure I'm doing something wrong.

Answer 1

\[\sum_{n = 0}^{\infty }(-1)^{n}(4x+1)^{n}\]

Answer 2

\[\sum_{n = 0}^{ \infty }(-1)^{n}(4x+1)^{n} , u_{n} = (4x+1)^{n}\]

Answer 3

\[\left| \sqrt[n]{(4x+1)^{n}} \right| = \left| (4x+1)^{\frac{n}{n}} \right| = \left| (4x+1) \right|\]