How to prove $\sqrt[n]{n}$ monotone decreases using inequality? there is a hint but I can't
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
73553
How is $a_n=(1+1/n)^n$ monotonically increasing and bounded by $3$?
25583
Show that the sequence $a_0 = 1$, $a_{n+1 }= \sqrt{2+a_n}$ is monotonically increasing
118244
An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
34491
Is there a way to show that $\sqrt{p_{n}} < n$?
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
139692
Proof of inequality using AM-GM inequality
86518
Does $X$ have a lower bound?
104125
How prove this inequality??
19078
Prove an interpolation inequality
2708
Inequality ${n \choose k} \leq \left(\frac{en}{ k}\right)^k$
35867
Squaring sides of an inequality
152764
Let ($x_n$) be a monotone sequence and contain a convergent subsequence. Prove that ($x_n$) is convergent.
100048
Got stuck in proving monotonic increasing of a recurrence sequence
17164
How do you show monotonicity of the $\ell^p$ norms?
42976
How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
120093
Proof of inequality $2(\sqrt{n+1}-\sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n} - \sqrt{n-1})$ using induction