Question

I need help with determining if infinite series are convergent or Divergent

I have the series

an = ((-1^(n))2n)/(n^(2) + 3n - 2012)

I already can tell that this series doesn't display monotonicity but I'm sure that is not enough to show that it is divergent anyone able to help me with this?

Answer 1

not just determining but proving as well

Answer 2

oh I just realized I can apply the rule

lim an / lim bn
n -> infinity n -> infinity

Answer 3

would that be a good first step?

Answer 4

so I get

lim (-1^(n))2n / infinity
n->infinity

how do I solve lim (-1^(n))2n
n->infinity

Answer 5

-1^(n) is always + or - 1 so I can just take the negative out of it? like so

lim -2(1^(n))n
n-> infinity
then I can go

-2(lim 1^(n)n)
n->infinity
=
-2(infinity)

Answer 6

so I'm left with

lim an = -5
n->infinity

Answer 7

sorry i mean -2

Answer 8

is that correct?