# Math Help - Determine whether the series is AC .. etc

1. ## Determine whether the series is AC .. etc

Hi
am studying for my incomplete exam after 10 days ..
I have problem with this question
http://www.sci.kuniv.edu.kw/content/...-April2007.pdf
Question 4-b

I know i will say |an| < an without cos 2n

and then ? which test i will use ?
I tested it with a couple with tests and i failed
help :/

2. $(2n)^n \cdot 2^{-n^2} \cdot \cos(2n) \le (2n)^n \cdot 2^{-n^2} = \left(\frac{2n}{2^n}\right)^n
$

nth root test ...

$\lim_{n \to \infty} \sqrt[n]{\left(\frac{2n}{2^n}\right)^n}$

$\lim_{n \to \infty} \frac{2n}{2^n} = 0$

series converges