Finding the Radius of Convergence for (sum from n=0 to infinity)7^(-n)x^(n)

[lmannoia]

Homework Statement

Find the radius of convergence for (sum from n=0 to infinity)7^(-n)x^(n).

Homework Equations

The Attempt at a Solution

The problem above it was a similar sum, (7^n)(x^n). That answer was that the radius of convergence was 1/7.
To do this one that I posted up there, I tried to use the Ratio Test...
7^(-n+1)x^(n+1) all over (7^-n)(x^n). I ended up getting 1/49, but that's wrong. Any idea of what I'm doing incorrectly, or do I just have the wrong approach to solve this one altogether?

 

[micromass]

Shouldnt that be 7^{-n-1} instead of 7^{-n+1}?

 

[lmannoia]

Oh wow, I can't believe I made that mistake. Thank you!

 

[lmannoia]

But wait, if you do 7^{-n-1}x^{n+1}/7^{-n}x^{n}, doesn't it get down to x/7? In which case, wouldn't R be 1/7?

 

[micromass]

Yes, the limit is 1/7. But to find the convergence radius, you have to invert that number. So the answer would be 7...