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

Apr 16, 2017

Diverges

#### Explanation:

Use the alternating series test. The ${\left(- 1\right)}^{n}$ goes away and we're left with:

${\lim}_{n \to 0} \left(1 - {n}^{2}\right)$

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.