How to Solve for n in a Power Series Limit?

[JRangel42]

Power Series:(n^n)*(x^n)

Homework Statement

The only step I'm having problem with on this problem is when I take the Lim n→∞ of the problem. I want to know how to cancel the n^n on the denominator during one of the steps.

Homework Equations

∞
Ʃ (n^n)*(x^n)
n=1

The Attempt at a Solution

lim n→∞ [(n+1)^(n+1)]*[x^(n+1)]/[(n^n)*(x^n)]

|x| lim n→∞ [(n+1)^(n+1)]/n^n

That's where I got stuck.

 

[deluks917]

(n+1)ⁿ⁺¹ / nⁿ = ( (n+1)ⁿ / nⁿ ) * (n+1). Can you see the limit now?

 

[JRangel42]

Oh, I definitely see it now! Thanks. (^o^)/

 

[Dick]

Can you show (n+1)^(n+1)/n^n>(n+1)??

 

[JRangel42]

Yeah, I can definitely do that part, I just I had a little trouble looking for the one little section I had trouble with.