Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises - Page 601: 37

$a_{n}=1+(-1)^{n}$

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