- #1

Mr Davis 97

- 1,462

- 44

## Homework Statement

Show that the series ##\displaystyle \sum_0^{\infty} (-1)^nn## diverges

## Homework Equations

## The Attempt at a Solution

It seems obvious that it diverges, for although the terms oscillate, they get bigger and bigger and never really cancel each other out. However, I am not sure how to show rigorously that it diverges, that is, using one of the tests from calc 2. I looked at a possible solution, and it said, using the Test for Divergence, we could conclude that since ##\displaystyle \lim_{n \to \infty} |(-1)^n n| = \infty##, the series diverges. But are we justified in using the absolute value? I thought that the test for divergence would just be ##\displaystyle \lim_{n \to \infty} (-1)^n n##, which doesn't seem to be able to be evaluated.