Is the sequence defined by the recurrence $a_{n+2}=\frac{1}{a_{n+1}}+\frac{1}{a_n}$ convergent?
34723
Proof of a limit for a recursively-defined sequence
153736
Question about convergence of a simple recursive sequence
145863
sequence of positive numbers satisfying $a_{n+1}=\frac{2}{a_n+a_{n-1}}$, prove it converges
60024
Proof that a sequence is convergent
132358
Is the sequence $a_{n+1}=a_n-\frac{1}{a_n}$, $a_0=2$ bounded?
120874
How to show if $|a_{n+1} - a_{n}| \le \frac{1}{2^n}$ then the sequence is Cauchy.
135018
Proving that a sequence has $a_n = a_{n+2}$ for $n$ sufficiently large.
61696
Prove that $\{x_1=1,\,x_{n+1}=\frac {x_n}2+\frac 1{x_n} \}$ converges when $n \to \infty$
33419
If $a_n$ is a strictly increasing unbounded sequence, does $\sum_n \frac{a_{n+1} - a_n}{a_n}$ diverge?
20136
Convergence of the sequence $ \sqrt {n-2\sqrt n} - \sqrt n $
90936
how prove $\sum_{n=1}^\infty\frac{a_n}{b_n+a_n} $is convergent?
141463
Convergence of $x_{n+1} = \frac12(x_n + \frac2{x_n}).$
155695
The convergence of a sequence
17201
$y_{2n}, y_{2n+1}$ and $y_{3n}$ all converge. What can we say about the sequence $ y_n$?
60405
Showing a recursive sequence isn't bounded $a_{n+1}=a_n+\frac 1 {a_n}$
8715
Let $(a_n)_n$ be a convergent sequence of integers , what can we say about $(a_n)_n$
110680
Convergence of recursive sequence $a_{n+1} =\frac{ 1}{k} \left(a_{n} + \frac{k}{a_{n}}\right)$