Prove that the difference between Harmonic numbers not natural number
2932
How do I prove this sum is not an integer
20945
On a series involving harmonic numbers
87764
Prove that the difference between two rational numbers is rational
12488
Show that $\frac{uu_x + vv_x}{u^2 + v^2}$ is harmonic.
37855
Sums and harmonic series
53672
Convergence of a Harmonic Continued Fraction
109305
Non-existence of natural numbers such that $\sqrt{n} +\sqrt{n+1} <\sqrt{x} +\sqrt{y} <\sqrt{4n+2}$
97522
Calculating a limit with Harmonic number
78847
Bijection between Prime numbers and Natural numbers
121469
Proof of observations on natural numbers being expressed as differences of squares.
145519
Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
66380
Alternating harmonic sum $\sum_{k\geq 1}\frac{(-1)^k}{k^3}H_k$
145007
Two problems on real number series
12865
Prove that $\lim_{n\to\infty} H_n/n = 0$ ($H_n$ is the $n$-th harmonic number) using certain techniques
75640
Does the harmonic series converge if you throw out the terms containing a $9$?
97192
product of harmonic functions
139841
Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$