Prove that sequence $a_1 = \sqrt{2}$, $a_{n+1} = \sqrt{2 + a_n}$ is bounded above by 3
27284
Show that the sequence $\sqrt{2}, \ \sqrt{2+\sqrt{2}}, \ \sqrt{2+\sqrt{2+\sqrt{2+}}}...$ converges and find its limit.
120093
Proof of inequality $2(\sqrt{n+1}-\sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n} - \sqrt{n-1})$ using induction
71639
Proof $(1+1/n)^n$ is an increasing sequence
37906
Prove $s_n$ is a Cauchy sequence for $|s_{n+1}-s_n|\lt2^{-n}$
17289
prove $\sqrt{a_n b_n}$ and $\frac{1}{2}(a_n+b_n)$ have same limit
111449
Prove there is an increasing sequence ($s_n$) of points in $S$ such that $\lim s_n = \sup S$.
120648
Proof Check: Every Cauchy Sequence is Bounded
12031
Asymptotic behavior of the sequence $a_n=\sqrt{n+a_{n-1}}$
46830
Prove that the sequence $a_{n+1} =\frac{1}{2}\left(a_{n}+\frac{c}{a_{n}}\right)$ is convergent and find its limit
69717
Find limit of recursive sequence $a_{n+1} =\sqrt{2+ \sqrt{a_n} }.$
100580
Proof that a sequence converges.
49828
Show that the sequence $\sqrt{2},\sqrt{2\sqrt{2}},\sqrt{2\sqrt{2\sqrt{2}}},...$ converges and find its limit.
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
54659
How prove that $(a_{n})_{n \in \mathbb{N}}$ is convergent with $a_{0}=1$, $a_{n+1}= \sqrt{2a_{n}}$?
46685
Show that the sequence $a_1=1$, $a_2=2$, $a_{n+2} = (a_{n+1}+a_n)/2$ converges by showing it is Cauchy
129393
Product of bounded and convergent to $0$ sequence is a convergent to $0$ sequence
111353
Show that $\{a_n\}$ defined by $a_{n+1}=\frac{a_n+2}{a_n+1}$ converges