Proving Whether an Alternating Series is Divergent or Convergent

[mundane]

Homework Statement

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

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

The Attempt at a Solution

I came up with this function:

a_n = 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?

 

[micromass]

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

 

[hedipaldi]

see answer 5

 

[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?

 

[hedipaldi]

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

 

[hedipaldi]

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