Prove ,by using the ε-definition, that the sequence :
$\displaystyle S_{n} = (-1)^n$ diverges
The ε-definition proves that some number L is the limit of a sequence. I've never heard that one can prove that a sequences diverges using that definition. We can prove that some number L is not the limit of the sequence, buy i've no idea of how can i use that definition to prove the divergence. Can you give me some hint?