Question:
List all the elements of each of the sets given below.
$G=\left\{x: x=\frac{1}{(2 n-1)^{\prime}} n \in N\right.$ and $1 \leq n \leq 5$
Solution:
Given:
$x=\frac{1}{2 n-1}$ and $1 \leq n \leq 5$
So, n = 1, 2, 3, 4, 5
If $n=1$, then $x=\frac{1}{2 n-1}=\frac{1}{2(1)-1}=\frac{1}{1}=1$
If $n=2$, then $x=\frac{1}{2 n-1}=\frac{1}{2(2)-1}=\frac{1}{4-1}=\frac{1}{3}$
If $n=3$, then $x=\frac{1}{2 n-1}=\frac{1}{2(3)-1}=\frac{1}{6-1}=\frac{1}{5}$
If $n=4$, then $x=\frac{1}{2 n-1}=\frac{1}{2(4)-1}=\frac{1}{8-1}=\frac{1}{7}$
If $n=5$, then $x=\frac{1}{2 n-1}=\frac{1}{2(5)-1}=\frac{1}{10-1}=\frac{1}{9}$
So, $G=\left\{1, \frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \frac{1}{9}\right\}$