## anonymous 5 years ago a_n= (-1)^n (n+4/n+1), determine whether the sequence converges or diverges

1. anonymous

divergent

2. anonymous

how did u get that lol?

3. anonymous

use absolute after that limit

4. anonymous

can u explain a little further

5. anonymous

let f(x)= a(n)= (-1)^n (n+4/n+1) |f(x)|= lim |(-1)^n (n+4/n+1)| --> lim 1^n(n+4/n+1) = 1 $\neq$ 0, means divergent

6. anonymous

Okay, alternating series test:$\sum_{n=1}^{\infty}(-1)^n*a_n = a_1-a_2+a_3-a_4+...$ converges if limit of a_n as n approaches infinity is 0. The limit is 1 as n approaches infinity in (n+4)/(n+1), which does not equal 0, hence, the series diverges.

7. anonymous

thanks ya'll