Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises - Page 601: 42

$S_{1}=-1$ $S_{2}=0$ $S_{3}=-1$ $S_{4}=0$ $S_{5}=-1$ $S_{6}=0$

We are given: $-1, 1, -1, 1$ ... We notice that the terms alternate between $-1$ and $1$: $a_{1}=-1=(-1)^1$ $a_{2}=1=(-1)^2$ $a_{3}=-1=(-1)^3$ $a_{4}=1=(-1)^4$ Therefore: $a_{n}=(-1)^{n}$ So: $a_{5}=-1$ $a_{6}=1$ We find the partial sums: $S_{1}=-1$ $S_{2}=-1+1=0$ $S_{3}=0-1=-1$ $S_{4}=-1+1=0$ $S_{5}=0-1=-1$ $S_{6}=-1+1=0$