- #1
Poopsilon
- 294
- 1
So basically I am trying to prove that the sum ∑1/2k from k=1 to n is a fraction of the form odd/even, that is to say that the denominator will contain more 2's than the numerator.
Now I'm almost positive this is true, and I suppose it might be more tractable to consider the stronger statement of taking the sum of some arbitrary set of fractions of the form 1/even and proving that that sum is a fraction of the form odd/even, ( although we would have to exclude the case of 1/2 + 1/2 and the others analogous to it ).
I actually want to prove this so I can prove a further statement and this step in my proof is really stumping me. Also note this isn't homework, its me satisfying my own personal interest in analytic number theory, so if you have any thoughts please don't feel the need to give cryptic overly ambiguous responses, thanks =].
Now I'm almost positive this is true, and I suppose it might be more tractable to consider the stronger statement of taking the sum of some arbitrary set of fractions of the form 1/even and proving that that sum is a fraction of the form odd/even, ( although we would have to exclude the case of 1/2 + 1/2 and the others analogous to it ).
I actually want to prove this so I can prove a further statement and this step in my proof is really stumping me. Also note this isn't homework, its me satisfying my own personal interest in analytic number theory, so if you have any thoughts please don't feel the need to give cryptic overly ambiguous responses, thanks =].