Proving that the sequence $a_1 = 4$, $a_{n+1} = \sqrt{a_{n} +20}$ converges and finding its limit
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
139356
How to find the limit of a sequence?
15319
Convergence of recurrence sequence
51502
To show for following sequence $\lim_{n \to \infty} a_n = 0$ where $a_n$ = $1.3.5 ... (2n-1)\over 2.4.6...(2n)$
89373
Convergence of $\frac{\sqrt{a_{n}}}{n}$
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?
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.
116414
Proving that the difference of the terms of a sequence, multiplied by $n$ converge
34025
Limit of the Sequence: $a_{n+1}=a_n+\frac{1}{a_n}$ with $a_1=1$
155695
The convergence of a sequence
55826
Convergence of sequence of real numbers and (sub)subsequence
30471
Show that $a_{n+1}= 1 + \frac{1}{a_n}$ converges.
33976
Prove that $\lim_{n \to \infty} \sqrt[n]{a} = 1$ using only the basic properties of sequences
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 $
112663
Let $a_n$ be a sequence s.t $a_1 > 0 \land a_{n+1} = a_n + \dfrac{1}{a_n}$. Prove that $a_n$ is increasing and tends to infinity
34723
Proof of a limit for a recursively-defined sequence
87834
How can we show that the following sequence converges?