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.