Answer
$S_{N}$ = $1$ if N odd, $0$ if N even
the sequence of partial sums diverges
Work Step by Step
$S_{1}$ = $(-1)^{1-1}$ = $1$
$S_{2}$ = $(-1)^{0}+(-1)^{1}$ = $0$
$S_{3}$ = $(-1)^{0}+(-1)^{1}+(-1)^{2}$ = $1$
$S_{4}$ = $(-1)^{0}+(-1)^{1}+(-1)^{2}+(-1)^{3}$ = $0$
$S_{N}$ = $1$ if N odd, $0$ if N even
Because the values of SN alternate between 0 and 1, the sequence of partial sums diverges
