How would we prove $\frac{n^2 - n}{2}$ is $\mathcal{O}(n^2)$?
92359
Big-O Notation Proof
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
151111
How do I show that $\frac{n}{\varphi(n)}=\sum\limits_{d \mid n} \frac{\mu^2(d)}{\varphi(d)}$?
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
87242
Ways to prove $ \int_0^\pi dx \frac{\sin^2(n x)}{\sin^2 x} = n\pi$
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
122932
When $(\mathbb{Q}(\zeta_n) : \mathbb{Q}) = 2$?
68385
Prove that $ \frac{n}{\phi(n)} = \sum\limits_{d \mid n} \frac{\mu^2(d)}{\phi(d)} $
28332
Proof of $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1}$
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
20271
Proving $\sum_{k=1}^n{k^2}=\frac{n(n+1)(2n+1)}{6}$ without induction
76977
Prove that $f(n)$ is the nearest integer to $\frac12(1+\sqrt2)^{n+1}$?
44391
How can I prove $n - 2\sqrt{n} = \Theta(n)$
71014
Prove that 2(nC0+nC2...nC$\frac{(N-1)}{2}$=$2^n$
1840
How can I prove that $\log^k(n) = O(n^\epsilon)$?
20964
Proof that $n^2 < 2^n$
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$