Show that the sequence is monotone and bounded.
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
10933
Let $(x_n)$ be a bounded but not convergent sequence. Prove that $(x_n)$ has two subsequences converging to different limits.
79266
Proving a sequence defined by a recurrence relation converges
14168
Prove the following sequence is a Cauchy Sequence
107311
Convergence of a sequence and some of its subsequences
119858
Proof: Every convergent sequence of real numbers is bounded
132358
Is the sequence $a_{n+1}=a_n-\frac{1}{a_n}$, $a_0=2$ bounded?
86465
Prove that every unbounded sequence contains a monotone subsequence that diverges to inifnity.
3211
The sequence $x_{n+1}=\frac{x_n}{2}-\frac{2}{x_n}, x_0>0$ is bounded?
144786
Show that the following inductively defined sequence converges and find its limit.
114975
Limit of sequences $V(n)$ and $U(n)$
152563
Set of discontinuity of monotone function is countable
153121
show that $\{x_n\}$ is a cauchy sequence
57095
How do I prove the sequence $x_{n+1}=\sqrt{\alpha +x_n}$, with $x_0=\sqrt \alpha$ converges? ( boundedness?)
58187
Solve the sequences inequality
108929
Proving the limit of a function of a sequence is equal to the function of the limit of that sequence
97047
Limit for sequence $a_{m+n}\leq a_m+a_n$