Let $k$ be a natural number, such that $k>1$.
Show that $1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{k}$ is not a natural number.
How I can prove this?
2026-03-28 06:30:17.1774679417
This number is not natural
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Hints:
Consider the highest power of $2$ that divides $k$, and the highest power of $2$ lesser than $k$.
Bertrand's postulate leads to a shorter solution. This result is highly non-trivial, though, and it is often not allowed in introductory courses of number theory.