# Homework Help: Alternating Series

1. Sep 19, 2010

### Autunmsky

Consider the series (to infinity; n=0) (-1/3)^n (x-2)^n

Find the intercal of convergence for this series.

To what function does this series converage over this interval?

I know this is an alternating series...I just don't know how to go about it. Thanks for you help.

** Should I do this like a partial sum? Do I just keep multiplying them together until they reach Zero *because then it has converaged? **

Last edited: Sep 19, 2010
2. Sep 19, 2010

### Staff: Mentor

It might be helpful to write this series as
$$\sum_{n = 0}^{\infty} (-1)^n \left(\frac{x - 2}{3}\right)^n$$

For some values of x, this is an alternating series, but for others, it's not.
What theorems do you know for determining whether a series converges?

3. Sep 19, 2010

### Autunmsky

a $$_{n+1}$$$$\leq$$ for all n

lim$$_{n\rightarrow\infty}$$ a$$_{n}$$ = 0

**sorry those are supposed to be lower subscripts**

4. Sep 19, 2010

### Staff: Mentor

You're still thinking that this is an alternating series. For some values of x (such as x = 0), it's NOT an alternating series.

Do you know any tests other than the alternating series test?

Last edited: Sep 19, 2010
5. Sep 19, 2010

### Autunmsky

Ratio Test so...lim |a $$_{n+1}$$| / |a$$_{n}$$|

6. Sep 20, 2010

### Staff: Mentor

OK, so what do you get if you use the Ratio Test?