Trivial limit ( 1 - (-x)^n ) / 1 + x

  1. 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 non-sense in this case.
     

    Attached Files:

  2. jcsd
  3. 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
     
  4. 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!
     
  5. Glad to have been of help! :smile:
     
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