Let {a_{n}} be a convergent sequence with limit L ∈ ℝ. Use properties of limits to compute $\displaystyle \lim_{n \rightarrow \infty } \frac{ {a}^2_{n} -1 }{{a}^2_{n} +1}} $

Attempt:

1. "Distribute" limit to numerator and denominator (allowed since {a_{n}} is convergent, so {a_{n}}^2-1 and {a_{n}}^2+1 are convergent.

2. "Distribute" limit to {a_{n}}^2 and -1 in the numerator and likewise for {a_{n}}^2 and 1 in the denominator.

3. Since {a_{n}} converges to L, we know {a_{n}}^2 converges even faster to L. Also, we know lim 1 is 1 and lim -1 is -1.

4. Thus, we have (L-1)/(L+1)

Question:

Is this an acceptable solution? I'm not sure if it's okay to have the answer in terms of "L".

Any help would be appreciated.