Question

How do you test for convergence of `Sigma (-1)^n(1-n^2)` from `n=[1,oo)`?

Answer 1

Diverges

Explanation:

Use the alternating series test. The `(-1)^n` goes away and we're left with:

`lim_(n->0) (1-n^2)`

Solving the limit will give you `1`. However, for an alternating series, the limit has to go to `0` in order for it to converge. Therefore, this diverges.