+1573 Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 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 3 fractions, and their product equals 4. What is the value of the first fraction he wrote?
+129933 (n+ 2)/(n ) * (n + 3) / (n + 1) * (n + 4) / ( n + 2) = 4 simplify as
(n + 3) *(n + 4) = 4 (n)(n + 1)
n^2 +7n +12 = 4n^2 + 4n
3n^2 - 3n - 12 = 0
n^2 - n - 4 = 0
n^2 - n +1/4 = 4
(n - 1/2)^2 = +/- 17/4
n = [1 + sqrt (17)] /2 or n = [ 1 -sqrt (17) ] /2
No integer values for numerator/denominator are possible
