Question

Set K consists of all fractions of the form x/(x+2) where x is a positive even integer less than 20. What is the product of all the fractions in Set K ?

Answer 1

`(1)/(231)`

Explanation:

The product of all the fractions in the Set k is

`(1)/(1+2) \cdot (2)/(2+2)\cdot(3)/(3+2)\cdot (4)/(4+2) \cdot\cdot\cdot(20)/(20+2)=\\\\\\(1\cdot2\cdot3\cdot4\cdot\cdot\cdot 20)/(3\cdot4\cdot5\cdot\cdot\cdot20\cdot21\cdot22)=(2)/(21\cdot22)=(1)/(21\cdot11)=(1)/(231)`