Question

Express in the roster form

$E=\{x|x=\frac{n}{n^2-1},2\le n\le 4,n\in N\}$

• A. $E=\{\frac{2}{3},\frac{3}{9},\frac{4}{16}\}$
• B. $E=\{\frac{2}{5},\frac{3}{4},\frac{4}{19}\}$
• C. $E=\{\frac{2}{3},\frac{3}{8},\frac{4}{15}\}$
• D. None of these
  

Answer 1

The correct option is C $E=\{\frac{2}{3},\frac{3}{8},\frac{4}{15}\}$

Since, $n\in N$ and $2\le n\le 4$

$\Rightarrow n=2,3,4$

$\text{when n=2;}x=\frac{n}{n^2-1}=\frac{2}{2^2-1}=\frac{2}{3}$

$\text{when n=3;}x=\frac{3}{3^2-1}=\frac{3}{9-1}=\frac{3}{8}$

$\text{when n=4;}x=\frac{4}{4^2-1}=\frac{4}{16-1}=\frac{4}{15}$

$E=\{\frac{2}{3},\frac{3}{8},\frac{4}{15}\}$