Question from Anonymous, a student:

How can you prove the following by induction:

Any fraction (A / B), where 0 < (A / B) < 1, can be expressed as a finite sum
(1 / c(1)) + (1 / c(2)) + (1 / c(3)) + ... + (1 / c(k)),
where c(1), c(2), ..., c(k) are natural numbers greater than 0.

[ex. (20 / 99) = (1 / 9) + (1 / 11)]