Computing the limit of a sequence

From Question:

For each real number x. determine if the sequence $$\left(\frac{1}{{1+x^{n}}}\right)^{\infty}_{n=1}$$ has a limit, and compute it when exist.

Let $a_n = \left(\frac{1}{{1+x^{n}}}\right)$
take limit ; $\lim_{n \to \infty} {a_n} = \lim_{n \to \infty} \frac{1} {{1+x^{n}}} = 0$
Given $\epsilon > 0$