Show that the sequence converges and what is it limit?$x_{n+1}=\frac{1}{2}(x_{n}+\frac{a}{x_n})$
34904
Proof of Convergence: Babylonian Method $x_{n+1}=\frac{1}{2}(x_n + \frac{a}{x_n})$
42300
Let the sequence be defined recursively $X_{n+1}=pX_{n}+q$ for p nonzero and $X_{1}$ arbitrary. In what conditions does the sequence converge?
19159
Convergence of $\frac{1}{(\ln n)^{\ln n}}$
54659
How prove that $(a_{n})_{n \in \mathbb{N}}$ is convergent with $a_{0}=1$, $a_{n+1}= \sqrt{2a_{n}}$?
47740
Let $x_1=a>0$ and $x_{n+1}=x_n+\frac{1}{x_n} \forall n\in \mathbb N$. Check whether the following sequence converges or diverges.
150000
Convergence of the sequence $\frac{1}{n\sin(n)}$
12480
Convergence of $\sum_{n=1}^{\infty} \frac{\frac{1}{2}+(-1)^n}{n}$
74522
Convergence of a sequence, $a_n=\sum_1^nn/(n^2+k)$
79877
Show convergence and calculate the limit: $\lim \limits_{n \to \infty}\sum \limits_{k=n}^{2n}\frac{k}{k^2+n^2}$
6815
$\lim_{n \rightarrow\infty} ~ x_{n+1} - x_n= c , c > 0$ . Then, is $\{x_n/n\}$ convergent?
50087
Convergence of $a_{n+1}=\frac{1}{1+a_n}$
53105
How to prove that this sequence converges? $\sum_{n=1}^{\infty} \frac{1}{n\ln^2(n)}$
12914
What's the limit of the sequence $\lim\limits_{n \to\infty} \frac{n!}{n^n}$?
141463
Convergence of $x_{n+1} = \frac12(x_n + \frac2{x_n}).$
57095
How do I prove the sequence $x_{n+1}=\sqrt{\alpha +x_n}$, with $x_0=\sqrt \alpha$ converges? ( boundedness?)
49507
Is this sequence convergent?
20909
For each positive integer $n$, let $x_n=1/(n+1)+1/(n+2)+\cdots+1/(2n)$. Prove that the sequence $(x_n)$ converges.