Finding the Limit of a Complex Sequence

Click For Summary

Homework Help Overview

The discussion revolves around finding the limit of a complex sequence defined by a(n)=[n+(-1)^n. sqrt(n)]/[(n^2 +1)^1/2]. Participants are exploring the behavior of the sequence as n approaches infinity.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the potential use of l'Hospital's rule and question its applicability. There is also a consideration of the sequence's oscillatory behavior as n increases, with some participants attempting to clarify the reasoning behind the limit tending towards 1.

Discussion Status

The discussion is active, with participants sharing different approaches and questioning each other's reasoning. Some guidance has been offered regarding dividing the numerator and denominator by n to analyze the limit further.

Contextual Notes

There is an implicit assumption that the limit exists, and participants are navigating the complexities of the sequence's behavior without a definitive conclusion.

Fairy111
Messages
72
Reaction score
0

Homework Statement



What is the limit of the following sequence, if it exists?

Homework Equations



a(n)=[n+(-1)^n. sqrt(n)]/[(n^2 +1)^1/2]

The Attempt at a Solution



Can i use l'hospital's rule? Or if not, how should i do this particular question?
 
Physics news on Phys.org
I'd imagine as [tex]n \rightarrow \infty[/tex]?

In that case, looks like it's going to oscillate back and forth dwindling down to 1.
 
Yea...as n tends to infinity. What were your steps to working out that it tends towards 1?
 
Divide the numerator and the denominator by n. Think about the behavior of each term.
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 17 ·
Replies
17
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K