Limit of a recursive sequence $a_{n+1}=\frac{1}{2}\left(a_n + \frac{5}{a_n}\right)$
34904
Proof of Convergence: Babylonian Method $x_{n+1}=\frac{1}{2}(x_n + \frac{a}{x_n})$
68609
Let $a_{n+1}=\sqrt{a_1+a_2+\cdots+a_n}$ .Prove that $ \lim\limits_{n \rightarrow \infty} \frac{a_n}{n}=\frac{1}{2}$
51502
To show for following sequence $\lim_{n \to \infty} a_n = 0$ where $a_n$ = $1.3.5 ... (2n-1)\over 2.4.6...(2n)$
15982
Limit of $b_n$ when $b_n=\frac{a_n}{n}$ and $\lim\limits_{n\to\infty}(a_{n+1}-a_n)=l$
102523
Show that $\lim\limits_{n \to \infty} \sup\limits_{k \geq n} \left(\frac{1+a_{k+1}}{a_k}\right)^k \ge e$ for any positive sequence $\{a_n\}$
50087
Convergence of $a_{n+1}=\frac{1}{1+a_n}$
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
119145
$\lim\limits_{n\rightarrow\infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$
88782
Finding the limit of $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$
94409
showing that the sequence $a_n=1+\frac{1}{2}+...+\frac{1}{n} - \log(n)$ converges
18675
$\{a_n\}$ sequence $a_1=\sqrt{6}$ for $n \geq 1$ and $a_{n+1}=\sqrt{6+a_n}$ show it that convergence and also find $\lim_{x \to \infty} \{a_n\}$
28669
Find limit of the following sequence: $\frac{\log(n+1)}{\log(n)}$?
17779
Proving the Limit of a Sequence of without the Dominated Convergence Theorem
86205
Evaluating the limit of a sequence given by recurrence relation $a_1=\sqrt2$, $a_{n+1}=\sqrt{2+a_n}$. Is my solution correct?
121774
Prove that $ \left(a_{n}\right)_{n=1}^{\infty} $ converges when $|a_{n+1}-a_{n}|<q|a_{n}-a_{n-1}|$ for $ 0<q<1 $
49497
$\lim a_n = 0$ if $\left|\frac{a_{n +1}}{a_n}\right|\to L < 1$
132358
Is the sequence $a_{n+1}=a_n-\frac{1}{a_n}$, $a_0=2$ bounded?