Are there 21 different positive whole numbers such that the sum of their reciprocals is 1?
I'm not sure about this question
Yes.
1/2+1/3 = 5/6
$\displaystyle 1/2+1/3+\frac{1/2+1/3}{6}$ = 35/36
$\displaystyle 1/2+1/3+\frac{1/2+1/3}{6}+\frac{\frac{1/2+1/3}{6}}{6}$ = $\displaystyle \frac{6^3-1}{6^3}$
We can keep doing this forever so the sum of any even number of reciprocals of natural numbers can represent $\displaystyle \frac{6^n-1}{6^n}$
Adding a last number of 1/6^n produces 1, so the sum of any odd number of reciprocals of 1atural numbers can be 1