Can every rational number be represented as a finite sum of reciprocal numbers? You are only allowed to use each reciprocal number one time per expression (So for example 3/2 cannot be 1/2+1/2+1/2).

You could then express these numbers in a kind of "binary-harmonic" where a 1 in the nth place from the right denotes adding 1/n. E.g 17/10 could be 10011 as it is 1+1/2+1/5.

Thanks in advance!

Can every rational number be represented as a finite sum of reciprocal numbers? You are only allowed to use each reciprocal number one time per expression (So for example 3/2 cannot be 1/2+1/2+1/2).

You could then express these numbers in a kind of "binary-reciprocal" where a 1 in the nth place from the right denotes adding 1/n. E.g 17/10 could be 10011 as it is 1+1/2+1/5.

Thanks in advance!

Can every rational number be represented as a finite sum of harmonic numbers? You are only allowed to use each harmonic number one time per expression (So for example 3/2 cannot be 1/2+1/2+1/2).

You could then express these numbers in a kind of "binary-harmonic" where a 1 in the nth place from the right denotes adding 1/n. E.g 17/10 could be 10011 as it is 1+1/2+1/5.

Thanks in advance!

Can every rational number be represented as a finite sum of reciprocal numbers? You are only allowed to use each reciprocal number one time per expression (So for example 3/2 cannot be 1/2+1/2+1/2).

You could then express these numbers in a kind of "binary-harmonic" where a 1 in the nth place from the right denotes adding 1/n. E.g 17/10 could be 10011 as it is 1+1/2+1/5.

Thanks in advance!