Show $a_{n+1} \geq \sqrt{B}$
31174
Find the limit if it exists of $S_{n+1} = \frac{1}{2}(S_n +\frac{A}{S_n})$
63124
Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
53584
Inequality. $(n+1)\left(a^{n+1}+b^{n+1}\right) \geq (a+b)\left(a^n+a^{n-1}b+\ldots+b^{n}\right). $
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
17289
prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
73987
Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$
55266
Prove that $(n+1)^{n-1}<n^n$
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
16634
How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$?
25583
Show that the sequence $a_0 = 1$, $a_{n+1 }= \sqrt{2+a_n}$ is monotonically increasing
121107
Proof by induction: $n^{n+1} > (n + 1)^n$, $(1 + x)^n \ge 1 + nx$, other inequalities
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
40700
Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$
55582
How can I show that $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt\ldots}}}$ exists?
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$