Answer
$S_{100}=0.$
$S_{101}=-1$
Work Step by Step
We have to find $S_{100}$ and $S_{101}$ for the sequence in which $a_n=(-1)^n$.
All even terms of the sequence are $1$ and all odd members are $-1$.
$-1,1,-1,1,-1,1,\cdots$
For $S_{100}$ we have half even and half odd terms in the sequence. We group them in pairs and we get:
$S_{100}=(-1+1)+(-1+1)+\cdots+(-1+1)=50(0)=0.$
For $S_{101}$ we have
$S_{101}=S_{100}+a_{101}=0+(-1)^{101}=-1.$
So $S_{101}=-1$
