Math Help - easy convergence question

This question seems like it should be so easy, but I just can't quite get there:

Use the fact that to deduce that .

So far this is what I have but I have a feeling i'm going about it the wrong way:

By algebra of limits:
So .
But from here I can't see how I can get the answer required.

Substitute and simplify (if you know the limit holds for positive and negative n).

For your solution

Now use the substitution

Cheers