Determine if an infinite series is con- or divergent Consider the following infinite series: $$\sum_{n=1}^\infty\frac{(-1)^n}{4n+(-1)^n}$$ I need to determine whether this sum converges or diverges. The root and ration test were inconclusive as I've tried them and by now I could not come up with a suitable comparable sum. My best guess by now is that it diverges.

Let,

$ a_n=\frac{1}{4n+(-1)^n}$

Note that sequence $\\{a_n\\}$ is monotonically decreasing and $a_n \to 0$.

Hence by Leibniz’s test, above series converges.