# Thread: Epsilon-n0 definition of convergence of a sequence

1. ## Epsilon-n0 definition of convergence of a sequence

Use the epsilon-n0 definition of convergence of a sequence to prove that $\lim_{n \rightarrow \infty } \frac{ {a}^2_{n} -1 }{{a}^2_{n} +1}}$ = L ℝ.

I'm very new to epsilon-
n0 proofs. Can someone help me get started? I substituted L for the actual value of the limit as I'm waiting to see what the actual value is (not sure if it can be in terms of L).

2. ## Re: Epsilon-n0 definition of convergence of a sequence

It would help if you would go back and check the problem again because what you have written doesn't make much sense. You can't prove that " $\frac{a_n^2- 1}{a_n^2+ 1}= L$" without knowing what the $a_n$ are. Perhaps you were asked to show that if that limit exists, then the limit of the $a_n$ exists? Or vice versa?