How to prove {$a_n$ } is increasing where $a_1 = \sqrt{2}$ and $a_{n+1} = \sqrt{ 2+ a_n}$
86205
Evaluating the limit of a sequence given by recurrence relation $a_1=\sqrt2$, $a_{n+1}=\sqrt{2+a_n}$. Is my solution correct?
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
76696
Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
118244
An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
44391
How can I prove $n - 2\sqrt{n} = \Theta(n)$
25775
How to prove $(1+1/x)^x$ is increasing when $x>0$?
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
78309
On an expansion of $(1+a+a^2+\cdots+a^n)^2$
9134
Suppose $\sum{a_n}$ converges. How do I prove that $\sum{\frac{\sqrt{a_n}}{n}}$ converges
63523
$|a_{n+1}-a_n| \leq \frac{1}{2} |a_{n}-a_{n-1}|$. Prove $(a_n)$ is Cauchy
114506
Expansion of $(1+\sqrt{2})^n$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$