Challange Problem; for those who have never seen it, try this by yourselves.
Prove that for , the sum is not an integer.
Moderator approved CB
Uuh?? We don't need the preceeding part to "...hence not integer" to conclude this: it must be obvious that it is not an integer since for ...and
thus your conclusion doesn't follow: for example, aren't integers, but are.
The proofs I know of this aren't hard but can be tricky. Hints for the most elementary one (that I know, of course):
If . Choose now , and now divide and sum and stuff.
Well for 1/1 + 1/2 + 1/4 +1/8 converges to two. 1/3 + 1/9 + 1/27 converges as well. This problem is really just asking if the series 1/p converges. P = prime
I am sure that this harmonic series diverges, but I really don't know how to prove it. And if it diverges, it does not converge on an integer.