Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises - Page 600: 5

$a_1=\frac{1}{3}$ $a_2=\frac{1}{5}$ $a_3=\frac{1}{7}$ $a_4=\frac{1}{9}$ $a_{100}=\frac{1}{201}$

We are given: $a_{n}= \frac{1}{2n+1}$ We evaluate: $a_1=\frac{1}{2(1)+1}=\frac{1}{3}$ $a_2=\frac{1}{2(2)+1}=\frac{1}{5}$ $a_3=\frac{1}{2(3)+1}=\frac{1}{7}$ $a_4=\frac{1}{2(4)+1}=\frac{1}{9}$ $a_{100}= \frac{1}{2(100)+1}=\frac{1}{201}$