Proof $\frac{1}{2}+\frac{1}{3}+....\frac{1}{n}$ is not an integer for integer $n>1$
46946
Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer?
105117
$1 + \frac{1}{3}\frac{1}{4} + \frac{1}{5}\frac{1}{4^2} + \frac{1}{7}\frac{1}{4^3} + ..........$
68400
Proof that $\frac{(2n)!}{2^n}$ is integer
63474
Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
156607
Show that $L_p =\frac{1^p+2^p+3^p+...+(p-1)^p}{p}$ is an integer and generalize the integer for all odd integers p
15164
Proof of $\sum^{2N}_{n=1} \frac{(-1)^{n-1}}{n} = \sum^{N}_{n=1} \frac{1}{N+n}$
20593
Show that if $a \neq b$ and a and b are positive then $\frac{a}{b}+\frac{b}{a}$ is never an integer
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
80216
Prove if $n \in \mathbb N$, then $\frac{1}{2!}+\cdots+\frac{n}{(n+1)!}=1-\frac{1}{(n+1)!}$
148647
If $\dfrac{4x^2-1}{4x^2-y^2}$ is an integer, then it is $1$
91105
For every $n\ge3$ there exists $n$ different integers $a_1,...,a_n$ so that $\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_n}=1$
144836
How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer?
158210
showing $\arctan(\frac{2}{3}) = \frac{1}{2} \arctan(\frac{12}{5})$
2932
How do I prove this sum is not an integer
88292
Prove by induction that $\sum\limits_{i=1}^n \frac{1}{n+i} \leq \frac{3}{4}$
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1