Question

is this convergent or not?

Answer 1

\[\sum_{n=o}^{\infty} (-1)^n(9)^n\]

Answer 2

You'll want to use the alternating series test for this. Are you familiar with it?

Answer 3

Not really

Answer 4

I think I got it. It's divergent, right?

Answer 5

I actually slightly misspoke earlier. It would be far easier to show that \[\large \lim_{n\rightarrow \infty}(-1)^n 9^n \neq0\]If this is true, then it diverges.

Answer 6

And even for this, we only have to prove that \[\large \lim_{n\rightarrow \infty}|(-1)^n 9^n |=9^n\neq0\]

Answer 7

This last statement is pretty straightforward to show that it's not 0.

Answer 8

Thank you @KingGeorge! :)

Answer 9

You're welcome.

Answer 10

And you were correct. It is divergent.