Question: Determine whether the following series converge absolutely, converge conditionally or diverge

$$\sum\_{1}^{+ \infty}\frac{1}{n! + n}$$
I tried using the ratio test but i can seem to find the value of limit. For comparison test there seems to be no other suitable series to be compared with. Divergence test does not work either because limit will be zero

Answer: 
$$0 \leq \sum\_{n = 1}^{k}\frac{1}{n! + n} \leq \sum\_{n = 1}^{k}\frac{1}{n!}$$ and the series $\sum\_{n = 1}^{+ \infty}\frac{1}{n!}$ is convergent by the ratio test
Well, for $n \geq 1 $,

$$ n! + n \geq 2^n \implies \frac{1}{n!+n} \leq \frac{1}{2^n} $$

Now, compare!