Question

describe in set builder form {1/2,2/5,3/10,4/17,5/26,6/37,7/50}

Answer 1

Answer:

The set builder form is

$X=\{\frac{n}{n^2+1}: 1\leq n \leq 7\}$  

Step-by-step explanation:

Given the set in roaster for i.e

$\{\frac{1}{2}, \frac{2}{5}, \frac{3}{10}, \frac{4}{17}, \frac{5}{26}, \frac{6}{37}, \frac{7}{50}\}$

we have to describe the above set in set-builder form

Let the set be X

$X=\{\frac{1}{2}, \frac{2}{5}, \frac{3}{10}, \frac{4}{17}, \frac{5}{26}, \frac{6}{37}, \frac{7}{50}\}$

$\frac{n}{n^2+1}$

$n=1; \frac{n}{n^2+1}=\frac{1}{1+1}=\frac{1}{2}$

$n=2; \frac{n}{n^2+1}=\frac{2}{2^2+1}=\frac{2}{5}$

$n=3; \frac{n}{n^2+1}=\frac{3}{3^2+1}=\frac{3}{10}$

$n=4; \frac{n}{n^2+1}=\frac{4}{4^2+1}=\frac{4}{17}$

$n=5; \frac{n}{n^2+1}=\frac{5}{5^2+1}=\frac{5}{26}$

$n=6; \frac{n}{n^2+1}=\frac{6}{6^2+1}=\frac{6}{37}$

$n=7; \frac{n}{n^2+1}=\frac{7}{7^2+1}=\frac{7}{50}$

Hence, the set builder form is

$X=\{\frac{n}{n^2+1}: n \in N, 1\leq n \leq 7\}$

which is required form

Answer 2

The set builder form for the expression {1/2,2/5,3/10,4/17,5/26,6/37,7/50} is  $X=\left\{\frac{n}{n^{2}+1}: 1 \leq n \leq 7\right\}$

Step-by-step explanation:

Given Data

{1/2,2/5,3/10,4/17,5/26,6/37,7/50}

To find the set builder form for the given expression

From the given expression it is clear that the denominator is equal to sum of 1 and square of numerator

Denominator = (Numerator)² + 1

If we consider numerator as 'n' then the denominator is n²+1

Then the given condition {1/2,2/5,3/10,4/17,5/26,6/37,7/50} is the from of $[\frac{n}{n^2 + 1} ]$ and the value of 'n' varies from 1 to 7

If $n = 1 ; ( n^2 + 1) = 2 ; \frac{n}{n^2 + 1} = \frac{1}{2}$

$n = 2 ; ( n^2 + 1) = 4+1 =5 ; \frac{n}{n^2 + 1} = \frac{2}{5}$

$n = 3 ; ( n^2 + 1) = 9+1 =10 ; \frac{n}{n^2 + 1} = \frac{3}{10}$

$n = 4 ; ( n^2 + 1) =16+1 =17 ; \frac{n}{n^2 + 1} = \frac{4}{17}$

$n = 5 ; ( n^2 + 1) =25+1 =26 ; \frac{n}{n^2 + 1} = \frac{5}{26}$

$n = 6 ; ( n^2 + 1) =36+1 =37 ; \frac{n}{n^2 + 1} = \frac{6}{37}$

$n = 7 ; ( n^2 + 1) =49+1 =50 ; \frac{n}{n^2 + 1} = \frac{7}{50}$

The set builder form for the given condition {1/2,2/5,3/10,4/17,5/26,6/37,7/50} is $X=\left\{\frac{n}{n^{2}+1}: 1 \leq n \leq 7\right\}$

To Learn More...

1) A={1/2,2/5,3/10,4/17,5/26} write this set in set builder form

  https://brainly.in/question/5755141

2) Find set builder form A={2,5,10,17,26}

   brainly.in/question/1437720