Limits of Sequences

  • Thread starter Bashyboy
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  • #1
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Homework Statement


[itex]\stackrel{lim}{n\rightarrow \infty} (-1)^n \frac{n}{n + 1}[/itex]


Homework Equations





The Attempt at a Solution


The answer is that the limit oscillates between -1 and 1, but I was wondering if there was an analytic was of showing this.
 

Answers and Replies

  • #2
LCKurtz
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Homework Statement


[itex]\stackrel{lim}{n\rightarrow \infty} (-1)^n \frac{n}{n + 1}[/itex]


Homework Equations





The Attempt at a Solution


The answer is that the limit oscillates between -1 and 1, but I was wondering if there was an analytic was of showing this.
Well, you know the sign alternates. What happens if you divide the numerator and denominator of your fraction by n? What happens then as ##n\to\infty##?
 
  • #3
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Ah, yes, I see. Thank you.
 
  • #4
22,089
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Writing limits in LaTeX looks better with the following code:

Code:
\lim_{n\rightarrow \infty}
There is no need for stackrel and such.
 

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