Show that $\frac{x(x-1) \dots (x-n+1)}{n!} \in \mathbb{Z}$ with $x \in \mathbb{Z}$
1507
The product of $n$ consecutive integers is divisible by $n$ factorial
89728
Prove that $1<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}$
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
112512
How to prove that there are finitely many $n$ such that $f(1+1/n) = \frac{1}{n+1}$?
100080
Proving with induction $(1-x)^n<\frac 1 {1+nx}$
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
128415
Prove that $1<\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\dots+\frac{1}{3001}<\frac43$
156356
Proof that $x^n+\frac{1}{x^n}\in \mathbb Z$ by complete induction
46431
Proof that $\sum\limits_i \frac{(p-1)!}i$ is divisible by $p$
34349
Prove that $\frac{1}{1+x_1}+\frac{1}{1+x_2}+\cdots+\frac{1}{1+x_n} \geq \frac{n}{\sqrt[n]{x_1x_2\cdots x_n}+1}$
73191
Proving that $\frac{1}{1\cdot 2} + \frac{1}{2\cdot 3} + \frac{1}{3 \cdot 4} +\ldots + \frac{1}{n(n+1)} = \frac{n}{n+1}$
109760
Showing that the product of all $n$th Roots of Unity is $(-1)^{n+1}$
129801
Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$