Determine if series abs conv/cond conv/divergent

[MarkSA]

Hello,

Determine if the series is absolutely convergent, conditionally convergent, or divergent.

1) Series from n=1 to infinity of: [(-1)^(n+1) * n^2 * 2^n]/n!
Let a(sub n) = that mess
I'm trying to take the limit of [a(sub n + 1)/a(sub n)] to test it. I'm getting tripped up by the factorial.

I'm at the point where I have:
Lim as n-> infinity of: [2(n + 1)^2 * n!]/[n^2 * (n + 1)!]
How would I cancel out the factorials n! in the numerator and (n + 1)! in the denominator?

 

[PAULK]

Hello,

Determine if the series is absolutely convergent, conditionally convergent, or divergent.

1) Series from n=1 to infinity of: [(-1)^(n+1) * n^2 * 2^n]/n!
Let a(sub n) = that mess
I'm trying to take the limit of [a(sub n + 1)/a(sub n)] to test it. I'm getting tripped up by the factorial.

I'm at the point where I have:
Lim as n-> infinity of: [2(n + 1)^2 * n!]/[n^2 * (n + 1)!]
How would I cancel out the factorials n! in the numerator and (n + 1)! in the denominator?

IF that's all you want to do, notice that (n+1)! = (n+1) n!
and that should do the canceling for you.