Radius of Convergence for Ratio Test in Calculus Questions

[belvol16]

Homework Statement

Homework Equations

Ratio test.

The Attempt at a Solution

[/B]
I guess I'm now uncertain how to check my interval of convergence (whether the interval contains -2 and 2)...I've been having troubles with this in all of the problems given to me. Do I substitute -2 back into the original equation and see if it is convergent or divergent?

 

[PeroK]

Homework Statement

View attachment 110223

Homework Equations

Ratio test.

The Attempt at a Solution

View attachment 110224 [/B]
I guess I'm now uncertain how to check my interval of convergence (whether the interval contains -2 and 2)...I've been having troubles with this in all of the problems given to me. Do I substitute -2 back into the original equation and see if it is convergent or divergent?

Yes, you have to check $x= \pm2$ explicitly.

 

[vela]

Homework Statement

View attachment 110223

Homework Equations

Ratio test.

The Attempt at a Solution

View attachment 110224[/B]

Either your work's wrong or there's a typo in the problem statement. Look at the exponent of $x$.