A Calculus Theorem Motivated by a Statistics Problem
David L. Farnsworth · College Mathematics Journal · 2004
two digits. For example, 1/97 = .01030927 ..., the powers of three. The Fibonacci numbers result from p = q = 1, co = 0, cl = 1, x = 10 in (2) as 10/89 = .11235 ... or using x = 100, we find 100/9899 = .0101020305081321 .... If we make up our own sequence 2, 5, 7, 12, 19,..., where p = q = 1, co = 3, cl = 2, and let x = 100, we find 203/9899 = .0205071219.... We can put an arithmetic progression into the digits of a decimal expansion by taking cl = a, C2 a + d, co = a d. Then Cn+2 = 2cn+1 cn, and p = 2, q = -1 in (2). Let x = 102, and expand fractions y/9801. The terms of the chosen arithmetic progression appear in blocks of two digits. Some examples are: