/sci/ - Science & Math

Hey, /sci/.

Is it possible to find a series of distinct fractions whose numerators are 1 denominators are odd so that the sum of the series is 1?

For example:
<div class="math">\frac{1}{3} + \frac{1}{9} + \frac{1}{11} = \frac{53}{99}</div>
The sum isn't 1, but is it possible to find such a combination of distinct unit fractions with all odd denominators that DOES sum to 1?

Is there no such think as a length that is an irrational number? Does that mean there can never be a perfect third of pizza? or pie?