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.
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
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!