Question

The roster form of the set $A=\{x:x=\frac{n}{2n+1},n\in N\text{and}n<4\}$ is ___. (Here, N stands for the set of natural numbers)

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

Answer 1

The correct option is B

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

Given, $n\in N,n<4$ and $x=\frac{n}{2n+1}.$
where $N$ stands for the set of natural numbers.

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

Substituting $n=1,2,3$ in $x=\frac{n}{2n+1},$ we get

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

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

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

$\therefore A=\{\frac{1}{3},\frac{2}{5},\frac{3}{7}\}$