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

1. Nov 27, 2011

### JRangel42

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

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Ʃ (n^n)*(x^n)
n=1

3. 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.

2. Nov 27, 2011

### deluks917

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

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

3. Nov 27, 2011

### JRangel42

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

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

4. Nov 27, 2011

### Dick

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

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

5. Nov 27, 2011

### JRangel42

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

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