Question

How do you determine whether the infinite sequence `a_n=(-1)^n` converges or diverges?

Answer 1

You can see that the sequence goes like this:
`{a_n}_{n=1}^{infty}={-1,+1,-1,+1,...}`

It simply alternates between -1 and +1, so it does not approach any single finite value; therefore, `lim_{n rightarrow infty}a_n` does not exist, which means that the sequence diverges.