# How do we find the radius of convergence?

##

I know that we have to use the ratio test to find the

#lim_(x->∞)Abs(U_(k+1)/U_k)#

and then make a conclusion on based on what we get. However, I'm having trouble evaluating the same and making a conclusion.

Please correct me if I'm wrong somewhere.

I know that we have to use the ratio test to find the

and then make a conclusion on based on what we get. However, I'm having trouble evaluating the same and making a conclusion.

Please correct me if I'm wrong somewhere.

##### 1 Answer

#### Explanation:

Apply the ratio test to the series:

Evaluate the ratio:

Now:

so, whatever is the value of

and the series is absolutely convergent.

We can conclude that the series converges for every