# Interval of convergence

1. Nov 24, 2006

### fsm

I just wanted to see if someone could verify my answers:

$$\\sum_{n=0}^\\infty \\frac{(x+7)^n}{sqrt(n)}$$
I get:
-8<x<-6

$$\\sum_{n=1}^\\infty \\frac{(-1)^n*x^2n}{n!}$$
This one I'm not sure of. When I take the limit I get 0. When I solve the inequality I get x. I can't find an example of this.

2. Nov 24, 2006

### fsm

This might be better:

3. Nov 24, 2006

1. correct

2. $$\sum_{n=1}^{\infty} \frac{(-1)^{n}x^{2n}}{n!}$$

$$|\frac{(-1)^{n+1}x^{2n+1}}{n!(n+1)}\frac{n!}{(-1)^{n}x^{2n}} = \frac{x}{n+1} \rightarrow 0$$. Thus the interval of convergence is $$(-\infty, \infty)$$

Last edited: Nov 24, 2006
4. Nov 24, 2006

### fsm

I don't understand your answer for #2. I got the same thing but how is this the interval of convergence?

5. Nov 24, 2006

### d_leet

What don't you understand about it?

6. Nov 24, 2006

### fsm

All the stuff to the right of the equal sign now just appeared. Thanks for the help.