Prove convergence of sequence defined by $a_{n+1}=\sqrt{3+a_n}$
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
19225
Let $\{a_n\}$ be defined as follows: $a_1 = 2$, $a_{n+1}=\frac{1}{3-a_n}$, if $n \geq 1$. Does $\{a_n\}$ converge?
101766
Recursive sequence convergence.: $s_{n+1}=\frac{1}{2} (s_n+s_{n-1})$ for $n\geq 2$, where $s_1>s_2>0$
112663
Let $a_n$ be a sequence s.t $a_1 > 0 \land a_{n+1} = a_n + \dfrac{1}{a_n}$. Prove that $a_n$ is increasing and tends to infinity
155695
The convergence of a sequence
145863
sequence of positive numbers satisfying $a_{n+1}=\frac{2}{a_n+a_{n-1}}$, prove it converges
69717
Find limit of recursive sequence $a_{n+1} =\sqrt{2+ \sqrt{a_n} }.$
61212
Using BMCT to prove the sequence $a_{n+1} = \sqrt{2 + a_n}$ is bounded and increasing.
93545
Showing the sequence converges $a_{1}=\frac{1}{2}$, $a_{n+1}=\frac{1}{2+a_{n}}$
27284
Show that the sequence $\sqrt{2}, \ \sqrt{2+\sqrt{2}}, \ \sqrt{2+\sqrt{2+\sqrt{2+}}}...$ converges and find its limit.
107311
Convergence of a sequence and some of its subsequences
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
30598
Showing that the sequence converges knowing that three other sequences converge
78886
Convergence of the sequence $\sqrt{1+2\sqrt{1}},\sqrt{1+2\sqrt{1+3\sqrt{1}}},\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1}}}},\cdots$
63612
Determine convergence of $\sum_{n=1}^{\infty}a_n$
147841
Please help prove that $(x_n)$ is a Cauchy sequence if $|x_{n+1} - x_n| \leq Cr^n$
40797
$(a_n+a_{n+1})$ is convergent implies $(a_n/n)$ converges to $0$