How to Solve for n in a Power Series Limit?

Click For Summary

Homework Help Overview

The discussion revolves around evaluating the limit of a power series involving the expression (n^n)*(x^n) as n approaches infinity. Participants are exploring the steps necessary to simplify the limit and address specific challenges encountered during the process.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the manipulation of the limit expression, particularly focusing on how to handle the term (n+1)^(n+1) in relation to n^n. There are inquiries about the validity of certain inequalities and simplifications.

Discussion Status

The conversation is active, with some participants expressing clarity on the limit after receiving input from others. However, there are still questions regarding specific steps and inequalities that need further exploration.

Contextual Notes

Participants are navigating the complexities of limits in the context of power series, with an emphasis on the behavior of terms as n approaches infinity. There is a noted challenge in simplifying expressions correctly, which may be influenced by the homework's constraints.

JRangel42
Messages
17
Reaction score
0
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.
 
Physics news on Phys.org


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


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


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


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

Similar threads

Interval of convergence of power series from ratio test
  • · Replies 2 ·
Replies
2
Views
2K
On the ratio test for power series
  • · Replies 2 ·
Replies
2
Views
2K
How to show that these sequences are summable?
  • · Replies 1 ·
Replies
1
Views
2K
Does this series converge uniformly?
  • · Replies 7 ·
Replies
7
Views
2K
How Do You Find a Recurrence Relation for a Power Series Solution of an ODE?
  • · Replies 8 ·
Replies
8
Views
3K
Prove that the limit as n->infinity of n^n/n! is infinity
  • · Replies 7 ·
Replies
7
Views
2K
Finding 2 solutions of this Bessel's function using a power series
  • · Replies 8 ·
Replies
8
Views
2K
Solve an ODE using Fourier series
  • · Replies 2 ·
Replies
2
Views
1K
Solving a Gaussian integral using a power series?
  • · Replies 9 ·
Replies
9
Views
3K
Prove that this series converges uniformly on R
  • · Replies 4 ·
Replies
4
Views
2K