Question

a_n= (-1)^n (n+4/n+1), determine whether the sequence converges or diverges

Answer 1

divergent

Answer 2

how did u get that lol?

Answer 3

use absolute after that limit

Answer 4

can u explain a little further

Answer 5

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

Answer 6

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.

Answer 7

thanks ya'll