# Total convergence of a function series

Let us consider the following function series:

$$\sum_{n=1}^{\infty} \frac{1}{n^x + n^{-x}}.$$

It seems that there is total convergence in $$(- \infty, -1-\delta] \cup [1+ \delta, + \infty)$$ for $$\delta > 0$$. Thank-you in advance for any help!