# reciprocals

• December 7th 2007, 06:51 PM
mr.toronto
reciprocals
Are there 21 different positive whole numbers such that the sum of their reciprocals is 1?

$1/2+1/3+\frac{1/2+1/3}{6}$ = 35/36
$1/2+1/3+\frac{1/2+1/3}{6}+\frac{\frac{1/2+1/3}{6}}{6}$ = $\frac{6^3-1}{6^3}$
We can keep doing this forever so the sum of any even number of reciprocals of natural numbers can represent $\frac{6^n-1}{6^n}$