Answer
Diverges
Work Step by Step
Formula to calculate the sum of a geometric series is:$S=\dfrac{a}{1-r}$
Here, the series $\lim\limits_{n \to \infty} (-1)^{n+1} n$ does not approach to zero and thus, possess no limit .
Also, when $n \to \infty$; we have $\lim\limits_{n \to \infty} (-1)^{n+1} n\ne 0$
Hence, the series $\lim\limits_{n \to \infty} (-1)^{n+1} (n)$ diverges.
