to Show that $\tau(n) \leq 2\sqrt n$.
52157
Prove that $d(n)\leq 2\sqrt{n}$
2708
Inequality ${n \choose k} \leq \left(\frac{en}{ k}\right)^k$
127102
Upper bound for $\sqrt[n]{n!}$
30386
Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
101176
Suppose that $(s_n)$ converges to s. Prove that $(s_n^2)$ converges to $s^2$
120309
Number Theory Inequality Proof
139674
Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
42976
How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
78985
Prove that: $\sqrt{2\sqrt{3\sqrt{4\cdots\sqrt{n}}}}<3,\,\forall n\in\mathbb N.$
837
Suppose that $(s_n)$ converges to $s$, $(t_n)$ converges to $t$, and $s_n \leq t_n \: \forall \: n$. Prove that $s \leq t$.
148582
Proof: $\|X\|_2\leq \sqrt{n}\|X\|_\infty$
80826
To prove $\left|\frac{p_n(z)}{q_m(z)}\right|\leq \frac{M}{|z|^{m-n}}$ for some $M>0$
121694
How to prove $\log n \leq \sqrt n$ over natural numbers?
118244
An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
66082
Using $\sqrt{1-t}\leq 1-\frac t2$ to show that $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n}\geq\frac1{2\sqrt n}$
95266
Show $|t|\leq \pi \Rightarrow |e^{it}-1|\geq 2|t|/ \pi$