Radius of Convergence Problem with Solution Attempt

[jegues]

Homework Statement

See figure attached for problem statement as well as my attempt.

Homework Equations

The Attempt at a Solution

See 2nd figure attached.

I don't know how to rid myself of that last n! I've got kicking around in the numerator.

Any ideas?

 

[jav]

Check your a_n+1 term. The [(n+1)!] should be squared.

 

[jegues]

Check your a_n+1 term. The [(n+1)!] should be squared.

Doh!

Thank you!

 

[jegues]

Just to make sure I finished the question off right, we should find that R = -1, correct?

Then the open interval of convergence is,

$$|x-7| < -1$$

or $$1 < x-7 < -1$$ or $$8 < x < 6$$