Question

The roster form of the set $\{x:x=\frac{n}{2n+1},\text{where}nϵN\text{and}n<4\}$ is ________.

• A. $\{\frac{1}{2},\frac{2}{3},\frac{3}{5}\}$
• B. $\{\frac{1}{3},\frac{2}{5},\frac{3}{7}\}$
• C. $\{\frac{1}{3},\frac{1}{5},\frac{1}{7}\}$
• D. $\{\frac{2}{3},\frac{2}{5},\frac{2}{7}\}$

Answer 1

The correct option is B

$\{\frac{1}{3},\frac{2}{5},\frac{3}{7}\}$

Given $nϵN$ and $n<4$

So, $n$ = 1, 2, 3.

Also, $x=\frac{n}{2n+1}$

Substituting $n$ = 1, 2, 3 we get,

$x=\frac{1}{2\left(1\right)+1}=\frac{1}{3}$

$x=\frac{2}{2\left(2\right)+1}=\frac{2}{5}$

$x=\frac{3}{2\left(3\right)+1}=\frac{3}{7}$

$\therefore$ The required set is $\{\frac{1}{3},\frac{2}{5},\frac{3}{7}\}$