Prove that any positive rational number can be expressed as a finite sum
. . of distinct terms of the harmonic series: .
I created my own Riddle.
I was going to take the following approach....but then I stopped....why?
We will show that is a vector space over spanned by the infinite dimensional set . But then I stopped there. Why?
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I am not going to answer your riddle because I already knew that, let someone else try.
No one took up the challenge?
This is an oldie from the study of "Eqyptian fractions".
There is no hide/show feature at this site, so here's the solution.
The rational number can be written: .
We eliminate the duplications by repeatedly using the identity:
. . .until all denominators are distinct.
Example:
. .
. .
Therefore: .