Answer
Diverges
Work Step by Step
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
As $n \to \infty$, the series $\lim\limits_{n \to \infty} (-1)^{n+1} n\ne 0$
Hence, the series $\lim\limits_{n \to \infty} (-1)^{n+1} n$ diverges
