# Proving Whether an Alternating Series is Divergent or Convergent

1. Nov 3, 2012

### mundane

1. The problem statement, all variables and given/known data

Determine an explicit function for this sequence and determine whether it is convergent.

an={1, 0, -1, 0, 1, 0, -1, 0, 1, ...}

3. The attempt at a solution

I came up with this function:

an = cos(nπ/2), and wrote that as sigma notation from n=0 to infinity. Is that good or should I use a quadratic?

I don't think it converges because it just oscillates and never changes, but how do I prove that?

2. Nov 3, 2012

### micromass

Staff Emeritus
Do you have to prove it using epsilon's and stuff??
If so, what is the definition of convergence? What is the negation?

3. Nov 3, 2012

### hedipaldi

Last edited: Nov 3, 2012
4. Nov 3, 2012

### mundane

I don't have to use epsilons. But I have to provide an equation showing it. And is the function I made satisfactory, or should I express it as a quadratic?

5. Nov 3, 2012

### hedipaldi

This sequence has 3 different limit points -1,0 and 1, therefore it does not have a limit.

6. Nov 3, 2012

### hedipaldi

If you reffer to the corresponding series,then it diverges because the general term does not converge to 0.