Finding the Radius of Convergence

"Find the radius of convergence for g(x) = the series x^n divided by 3n + 1, where n = 0 and goes to infinity. Be sure to check the endpoints for convergence, and state which tests you are using."

I'm pretty lost on this guys. My notes don't really elaborate on what the radius of convergence is or how you figure it out. Any help is really appreciated. Thanks in advance everyone!

Re: Finding the Radius of Convergence

Quote:

Originally Posted by

**bobsanchez** "Find the radius of convergence for g(x) = the series x^n divided by 3n + 1, where n = 0 and goes to infinity. Be sure to check the endpoints for convergence, and state which tests you are using."

Use the nth root test $\displaystyle \sqrt[n]{{\frac{{\left| x \right|^n }}{{3n + 1}}}} \to \left| x \right| < 1$.

Now solve that for x. BUT check the endpoints.

Re: Finding the Radius of Convergence

I'm sorry, but I still don't really understand. I don't know how to solve for x in that situation, or what that really means. I know it's dense of me, but this material hasn't been covered at all and I can't find a good source on it.

Re: Finding the Radius of Convergence

Quote:

Originally Posted by

**bobsanchez** I'm sorry, but I still don't really understand. I don't know how to solve for x in that situation, or what that really means. I know it's dense of me, but this material hasn't been covered at all and I can't find a good source on it.

You are expected to be able to do first year algebra before working with series.

Can you solve $\displaystyle |x|<1~?$

If not, you need to work on your basic algebra skills before you try to proceed with series.

Re: Finding the Radius of Convergence

Quote:

Originally Posted by

**Plato** You are expected to be able to do first year algebra before working with series.

Can you solve $\displaystyle |x|<1~?$

If not, you need to work on your basic algebra skills before you try to proceed with series.

What do I set it equal to to solve for the x in that formula you posted? That's what I don't understand.

Re: Finding the Radius of Convergence

Alright, sorry for wasting your time. I'll look elsewhere for help.

Re: Finding the Radius of Convergence

what do you know about the ratio test for convergence/divergence and using it to find the interval of convergence?

Re: Finding the Radius of Convergence

Quote:

Originally Posted by

**skeeter** what do you know about the ratio test for convergence/divergence and using it to find the interval of convergence?

I know the ratio test works for determining whether a series has convergence/divergence, but I'm not familiar with using it to determine the interval of convergence.

Re: Finding the Radius of Convergence

Re: Finding the Radius of Convergence

Quote:

Originally Posted by

**skeeter**

Nice, excellent video. So basically do the ratio test, and under those circumstances you can pull the x out, turn it into an inequality, and solve, then plug in to check endpoints...okay, I think I understand it now.

Thanks so much!