Question

Describe the following sets in Set-Builder form
$\{\frac{1}{2},\frac{2}{5},\frac{3}{10},\frac{4}{17},\frac{5}{26},\frac{6}{37},\frac{7}{50}\}$

Answer 1

Solution:-

$\{\frac{1}{2},\frac{2}{5},\frac{3}{10},\frac{5}{26},\frac{6}{37},\frac{7}{50}\}$

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

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

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$\frac{7}{50}=\left(\frac{7}{1+7^2}\right)$

Set-Builder form: $\{x:x=\frac{n}{1+n^2};n\in N\text{and}1\le n\le 7\}$