Show that the sequence $\sqrt{2}, \ \sqrt{2+\sqrt{2}}, \ \sqrt{2+\sqrt{2+\sqrt{2+}}}...$ converges and find its limit.
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?
79877
Show convergence and calculate the limit: $\lim \limits_{n \to \infty}\sum \limits_{k=n}^{2n}\frac{k}{k^2+n^2}$
70561
limit of the sequence $a_n=1+\frac{1}{a_{n-1}}$ and $a_1=1$
107735
What does the following sequence converge to?
17902
Prove or disprove: $\sum a_n$ convergent, where $a_n=2\sqrt{n}-\sqrt{n-1}-\sqrt{n+1}$.
55826
Convergence of sequence of real numbers and (sub)subsequence
60024
Proof that a sequence is convergent
89373
Convergence of $\frac{\sqrt{a_{n}}}{n}$
67638
Show that $x_{n+1}=x_n(2-ax_n)$ converges and find the limit
87834
How can we show that the following sequence converges?
149806
Is it possible to utilize the convergence of the sequence $z_{n+1}=a/(1+z_n)$ to prove that the sequence $x_{n+2} = \sqrt{x_{n+1} x_n}$ is convergent?
132140
Convergence of Sequence of Real Numbers
54659
How prove that $(a_{n})_{n \in \mathbb{N}}$ is convergent with $a_{0}=1$, $a_{n+1}= \sqrt{2a_{n}}$?
49507
Is this sequence convergent?
142509
If $\alpha\in (0,1]$ and $x_n=\alpha x_{n-1}+(1-\alpha)x_{n-2}$, show that the sequence $\{x_n\}$ is convergent.
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 $
86970
Let $\{x_n\}$ be a sequence in a metric space such that $\{x_{2n}\}$, $\{x_{2n+1}\}$ and $\{x_{3n}\}$ all convergent. Show that $\{x_{n}\}$ converges