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?
+128474 (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
