This sequence $\sqrt {a+\sqrt{a+\sqrt{a+\sqrt{a...}}}}$ is bounded?
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
27284
Show that the sequence $\sqrt{2}, \ \sqrt{2+\sqrt{2}}, \ \sqrt{2+\sqrt{2+\sqrt{2+}}}...$ converges and find its limit.
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
135155
Why is $\lim_{n \to +\infty }{\sqrt[n]{a_1 a_2 \cdots a_n}} =\lim_{n \to +\infty}{a_n}$
40797
$(a_n+a_{n+1})$ is convergent implies $(a_n/n)$ converges to $0$
37906
Prove $s_n$ is a Cauchy sequence for $|s_{n+1}-s_n|\lt2^{-n}$
11586
Sequences of Real Numbers in a closed bounded interval
33419
If $a_n$ is a strictly increasing unbounded sequence, does $\sum_n \frac{a_{n+1} - a_n}{a_n}$ diverge?
112430
Prove that sequence $ x_{(n+1)}= \frac {a}{1+x_n}$ is convergent to positive root of $x^2+x-a=0,$where $a >0$ and $x_1 >0$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
73080
Is the set of all bounded sequences complete?
73934
Subadditive sequences and the limit $\sup_{n\to\infty} a_n / n$
25674
Bounded sequence which is not convergent, but differences of consecutive terms converge to zero
119858
Proof: Every convergent sequence of real numbers is bounded
113151
Does $\sum\limits_{i=1}^{\infty}|a_i||x_i| < \infty$ whenever $\sum\limits_{i=1}^{\infty} |x_i| < \infty $ imply $(a_i)$ is bounded?
47922
Prove that the sequence $(a_n)$ defined by $a_0 = 1$, $a_{n+1} = 1 + \frac 1{a_n}$ is convergent in $\mathbb{R}$
112368
Is there a rule for $\sqrt{a+b}$?