Bunuel
Which of the following is closest to the difference between sum of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
(A) 2.82
(B) 2.72
(C) 1.82
(D) 1.72
(E) 0.82
product of all proper fractions in the form y/(y+1) = \(\frac{1}{2}*\frac{2}{3 }*\frac{3}{4}\).....
You can see denominator of 1st term is cancelled out with numrator of 2nd term
denominator of 2nd term is cancelled out with numrator of 3rd term
This will go on till infinity as there is no limit given to Y
Hence sum of product of all proper fractions in the form y/(y+1) =\( \frac{1}{infinity}\) = 0
Hence there is no as such differeance.
We need to find value of sum of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit.
Now , sum of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit = \(\frac{1}{2 }+ \frac{1}{3 }+ \frac{1}{4}+\)....
{We are not taking \(\frac{1}{1}\) ie. 1 as it is not proper fractions (fractions less than 1)}
=0.50+0.33+0.25+0.20+0.16+0.14+0.12+0.11+0.1....Value would reduce further We need to find closed value so will consider 1st 10 terms .
=
1.91Option C