Ratio Test for Radius of Convergence | Solving sum(5^n)((x-3)^n)/n"

[thomas12323]

Homework Statement

The problem is looking for the radius of convergence
sum(5^n)((x-3)^n)/n
n=1

Homework Equations

The Attempt at a Solution

 

[Mark44]

What work have you done in using the ratio test?

 

[thomas12323]

I broke it down to (x-3)n/(n+1)

 

[Mark44]

That's not right. What happened to the 5^n factor?
You should have this as part of your work.
\lim_{n \to \infty} \left(\frac{5^{n + 1}(x - 3)^{n + 1}}{n + 1}~\frac{n + 1}{5^n (x - 3)^n}\right )