A sequence satisfies $a_{n+2} = \frac{2}{a_{n+1}} + a_n$ where $a_1 = 1, a_2 = 2$. Find the value of $\frac{2^{2009}}{2011}a_{2012}$
126039
Find the value of the the term
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
81052
Determining a limit of parametrized, recursively defined sequence $a_{n+1}=1+\frac{(a_n-1)^2}{17}$
29170
Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$
126791
If $2a_{n+2} \le a_{n+1}+a_n$, then $\lim \sup a_n \le \frac23 a_2 + \frac13 a_1$
141463
Convergence of $x_{n+1} = \frac12(x_n + \frac2{x_n}).$
101766
Recursive sequence convergence.: $s_{n+1}=\frac{1}{2} (s_n+s_{n-1})$ for $n\geq 2$, where $s_1>s_2>0$
137027
Find the value of $\sum_{n=0}^\infty\frac{1}{9n^2+9n+2}$
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 $x_1 >0$
104494
$m$ doesn't come in the sequence $a_n=[n+\sqrt{n}+\frac{1}{2}]$ iff m is a perfect square
121554
Finding $\sum\frac{1}{2^n(n+1)}$
50087
Convergence of $a_{n+1}=\frac{1}{1+a_n}$
25426
A sum of series problem: $\frac{3}{1!+2!+3!} + \frac{4}{2!+3!+4!} + \cdots + \frac{2008}{2006!+2007!+2008!}$
110680
Convergence of recursive sequence $a_{n+1} =\frac{ 1}{k} \left(a_{n} + \frac{k}{a_{n}}\right)$
104268
Confusion on how to solve this question about sequences.
3211
The sequence $x_{n+1}=\frac{x_n}{2}-\frac{2}{x_n}, x_0>0$ is bounded?
74120
Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$