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Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is $1$ greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator of the previous fraction by $1$. He then multiplies all his fractions together. He has $20$ fractions, and their product equals $3$. What is the value of the first fraction he wrote?

 Jul 1, 2022
 #1
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+2

(N + 1)        (N + 2)       (N + 3)                     (N + 19)      (N + 20)

______ *   _______ * _______  *   ......  *    ________ * _______

     N             (N + 1)      (N + 2)                     ( N + 18)     (N + 19)

 

Note  that the product of all the  fractions will be

 

(N + 20) / N  =  3

 

N + 20  = 3N

 

20 =  2N

 

N = 10

 

The first fraction  was   (N + 1)  / N   =       11 /  10

 

 

cool cool cool

 Jul 1, 2022
 #2
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thank u

Guest Jul 1, 2022

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