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Trivial limit ( 1  (x)^n ) / 1 + x 
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#1
Jun1012, 04:15 AM

P: 2

1. The problem statement, all variables and given/known data
lim ( 1  (  x ) ^ n ) / ( 1 + x ) as n > infinity 2. Relevant equations I can't understand why this equals to 1 / ( 1 + x ) (No matter what power of " n " was x e.q: x ^ 2n or x ^ ( n ^ 2 ) 3. The attempt at a solution I have no clue what rule to apply. I thought it might be a case of using the lim ( 1 + 1 / n ) ^ n to get to " e " but this seems like a nonsense in this case. 


#2
Jun1012, 04:25 AM

P: 854

I think you first need to have a condition on x before that is true.
0 < x < 1, right? If so, anything between 0 and 1 raised to a power of infinity will tend to 0, as it gets smaller with each successive multiplication. [tex]\lim_{n\to \infty} x^n = 0[/tex] where 1<x<1 


#3
Jun1012, 04:28 AM

P: 2

Thank so much for the reply! Yes, x > 1 and x < 1 or 1 < x < 1 and now I understand why this is the result!
Thank you again! 


#4
Jun1012, 04:32 AM

P: 854

Trivial limit ( 1  (x)^n ) / 1 + x
Glad to have been of help!



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