Find the limit of the sequence $(a_n)_{n \ge 0}$ given that $a_{n+1}^2=a_na_{n-1}$ and $a_0=2,$ $a_1=16$.
57904
Recurrence relation with limit
142778
Finding $\lim_{n\to\infty}a_n$ if $a_0=a,a_1=b$ and $a_n=\frac{1}{2}(a_{n-1}+a_{n-2})$ where $a, b \in \mathbb{R}$
130693
Sequence such that $\lim\limits_{n\to \infty} \frac{x_1^2+x_2^2+...+x_n^2}{n}=0$
80440
Limit of $(x_n)$ with $0<x_1<1$ and $x_{n + 1} = x_n - x_n^{n + 1}$
5797
Limit of the sequence $a_n=\sqrt[n+1]{(n+1)!}-\sqrt[n]{n!}$
152525
If $b_n$ is a bounded sequence and $\lim a_n = 0$, show that $\lim(a_nb_n) = 0$
102425
Limit $ a_{n+1} = \frac{1}{3}(2a_n + \frac{5}{a_n^{2}}), a_1 > 0 $
60815
If $a_{n+1}=\cos(a_n)$ for $n\ge0$ and $a_0 \in [-\pi/2,\pi/2]$, find $\lim_{n \to \infty}a_n$ if it exists
47922
Prove that the sequence $(a_n)$ defined by $a_0 = 1$, $a_{n+1} = 1 + \frac 1{a_n}$ is convergent in $\mathbb{R}$
49828
Show that the sequence $\sqrt{2},\sqrt{2\sqrt{2}},\sqrt{2\sqrt{2\sqrt{2}}},...$ converges and find its limit.
29266
Limit of a sequence defined by recursive relation : $ a_n = \sqrt{a_{n-1}a_{n-2}}$
145863
sequence of positive numbers satisfying $a_{n+1}=\frac{2}{a_n+a_{n-1}}$, prove it converges
67638
Show that $x_{n+1}=x_n(2-ax_n)$ converges and find the limit
138052
How to work out the limit of  this bounded sequence?
132947
How to calculate the limit of $\frac{a_n}{n^2}$ for the sequence $a_{n+1}=a_n+\frac{2 a_{n-1}}{n+1}$?
19745
Let $a_n$ be a sequence such that: $ a_{n+1}-a_n \ge \frac{1}{n}$. prove that $\lim_\limits{n \to \infty} a_n = \infty$.
88782
Finding the limit of $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$