Egyptian Fractions are fractions expressed in the form of 1/n or as the sum of such fractions (1/a + 1/b + ...). For example, 2/3 would be expressed as 1/2 + 1/6.
(As found on the Rhind papyrus, 2/3 was one, if not the only, non-unit fraction used by the Egyptians.)

The following Egyptian Fractions correspond to the fractional portion of the first ten non-integer members of a "regular" series. (The "whole number" component of each member of the series is omitted and any series members without fractional components is likewise omitted).

What is the missing fraction in this sequence?

1/2 + 1/14
1/4 + 1/44
1/4 + 1/18 + 1/468
1/4 + 1/28
1/2
1/2 + 1/4 + 1/14 + 1/476
1/19
1/2 + 1/3 + 1/42
1/2 + 1/8 + 1/88
1/3 + ?

Well, I've got no idea where to start on figuring out the actual sequence, but here's the simplified versions of all those fractions:

1/2 + 1/14 = 4/7
1/4 + 1/44 = 3/11
1/5 + 1/33 + 1/2145 = 3/13
1/4 + 1/128 = 33/128
1/2
1/2 + 1/4 + 1/14 + 1/476 = 14/17
1/19
1/2 + 1/3 + 1/42 = 6/7
1/2 + 1/8 + 1/88 = 7/11

Interesting to note that we get primes in ascending order in the denominators: 7, 11, 13, 17, 19. Then the sequence repeats. What 128 and 2 are doing in between, I don't know. And of course there might be integer answers in between as well.

Posted by Jyqm on 2006-05-28 13:13:18