Find the radius of convergence of the Taylor series around x=0 for $$\ln(\frac{ 1 }{ 1-6x })$$.

What I've been able to do so far is find the taylor series for ln(x): $$(x-1)-\frac{ (x-1)^2 }{ 2 }+\frac{ (x-1)^3 }{ 3 }-\frac{ (x-1)^4 }{ 4 }+...$$

I also know that finding the radius of convergence means I need to use the ration test: $$\frac{ |a_{n+1}| }{ |a_n| }$$

What is the next step in solving this problem? I am not sure exactly how to determine what I should be plugging into the ratio test?

Question

Find the radius of convergence of the Taylor series around x=0 for $$\ln(\frac{ 1 }{ 1-6x })$$.

What I've been able to do so far is find the taylor series for ln(x): $$(x-1)-\frac{ (x-1)^2 }{ 2 }+\frac{ (x-1)^3 }{ 3 }-\frac{ (x-1)^4 }{ 4 }+...$$

I also know that finding the radius of convergence means I need to use the ration test: $$\frac{ |a_{n+1}| }{ |a_n| }$$

What is the next step in solving this problem? I am not sure exactly how to determine what I should be plugging into the ratio test?