Question

Write the set $\{\frac{1}{2},\frac{2}{5},\frac{3}{10},\frac{4}{17},\frac{5}{26},\frac{6}{37},\frac{7}{50}\}$ in the set -builder form.

Answer 1

As $2=1^2+15=2^2+110=3^2+1::50=7^2+1$

So, the above set in set builder form can be written as

$\{\frac{n}{n^2+1}:nϵN,1\underset{–}{<}n\underset{–}{<}7\}$