Taking the Limit As N -> Infinity

  • Thread starter Thread starter student45
  • Start date Start date
  • Tags Tags
    Infinity Limit
Click For Summary

Homework Help Overview

The discussion revolves around evaluating the limit of a mathematical expression as n approaches infinity, specifically focusing on the expression involving n raised to the power of n and its relation to x and e.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss factoring out terms and consolidating factors to simplify the limit. There is a focus on recognizing familiar forms, particularly the expression (1 + (1/n))^n.

Discussion Status

Participants are actively engaging with the problem, with some providing guidance on how to manipulate the expression. There is an acknowledgment of the relationship to e, although there is no explicit consensus on the final outcome.

Contextual Notes

Some participants question the assumptions regarding the limit's existence and the manipulation of the terms involved.

student45
Taking the Limit As N --> Infinity

[tex]\mathop {\lim }\limits_{n \to \infty } \frac{{n^n x}}{{(n + 1)^n }}[/tex]

Does this limit exist? Somehow it's supposed to come down to x/e
 
Last edited by a moderator:
Physics news on Phys.org
Factor out the x (the limit is with respect to n).

Consolidate the remaining factors into a term with a single exponent.

Perform a little magic inside the parentheses and look for something familiar.
 
Got everything except the magic... the goal is to get (1+(1/n))^n, right?
 
Well, that would be e. You want 1/e.
 
Doh! Thanks. Got it.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 20 ·
Replies
20
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K