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?
+307 \({d+1\over d} \times {d+2\over d+1} ... \times {d+20\over d+19}=3\)
The numerator of the first term cancels the denominator of the second, and so on until the numerator of the 19th term cancels the denominator of the 20th.
You are left with d+20/d =3
3d = d + 20
2d = 20
d = 10
The original fraction is d+1/d = 11/10
