Answer
The sequence appears divergent.
Work Step by Step
The sequence of the partial sums is given by $S_n=\sum_{k=1}^n(-1)^kk$.
Substituting $n=1,2,\ldots,8$, we get the first eight terms of the sequence of the partial sums
$S_1=-1$
$S_2=-1+2=1$
$S_3=-2$
$S_4=2$
$S_5=-3$
$S_6=3$
$S_7=-4$
$S_8=4$
Since $S_n$ contains a substring $-1,-2,-3,....$ going to $-\infty$ and a substring $1,2,3...$ going to $\infty$, the series appears divergent.
