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

Answer:

$\dfrac{1}{231}$

Step-by-step explanation:

The product of all the fractions in the Set k is

$\dfrac{1}{1+2} \cdot \dfrac{2}{2+2}\cdot\dfrac{3}{3+2}\cdot \dfrac{4}{4+2} \cdot\cdot\cdot\dfrac{20}{20+2}=\\\\\\\dfrac{1\cdot2\cdot3\cdot4\cdot\cdot\cdot 20}{3\cdot4\cdot5\cdot\cdot\cdot20\cdot21\cdot22}=\dfrac{2}{21\cdot22}=\dfrac{1}{21\cdot11}=\dfrac{1}{231}$