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

[davitz]

Homework Statement

lim ( 1 - ( - x ) ^ n ) / ( 1 + x ) as n -> infinity

Homework 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 )

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.

 

[Infinitum]

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.

$$\lim_{n\to \infty} x^n = 0$$

where -1<x<1

 

[davitz]

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!

 

[Infinitum]

Glad to have been of help!