how can I prove it is a convergent sequence and its limit is $\sqrt{a}$
34904
Proof of Convergence: Babylonian Method $x_{n+1}=\frac{1}{2}(x_n + \frac{a}{x_n})$
37394
How to find $\lim\limits_{n\to\infty} n·(\sqrt[n]{a}-1)$?
112595
Prove that the limit of this sequence is $\frac{1}{2}(1 + \sqrt{5})$
57095
How do I prove the sequence $x_{n+1}=\sqrt{\alpha +x_n}$, with $x_0=\sqrt \alpha$ converges? ( boundedness?)
33976
Prove that $\lim_{n \to \infty} \sqrt[n]{a} = 1$ using only the basic properties of sequences
30598
Showing that the sequence converges knowing that three other sequences converge
5728
How to prove $\lim_{n \to \infty} \sqrt{n}(\sqrt[n]{n} - 1) = 0$?
114315
The sequence 1/(n-1) is apparently unbounded yet convergent. What am I missing here?
143146
Help with completing the proof: Any unbounded sequence is either infinitely large or has a convergent subsequential limit
20136
Convergence of the sequence $ \sqrt {n-2\sqrt n} - \sqrt n $
87116
Prove $ \lim_{n\to \infty}\frac{n}{n+1} = 1$ using Cauchy (epsilon) definition of a limit of a sequence
7507
Proof that $\lim{a_n}=L$ when $n$ goes to infinity, then $\{a_n\}$ its a Cauchy Sequence
14175
$\sum_\limits{n=0}^{\infty} a_n$ converges $\implies \sum_\limits{n=0}^{\infty} a_n^2$ converges
142
Showing the sequence converges to the square root
7815
Prove that $\lim_{n\to\infty}a_n^2=a^2$ when ${a_n}$ is a sequence in $\mathbb{R}$ with $\lim_{n\to\infty}a_n=a$
65592
Convergence of $a_n=(1/2)^{(1/3)^{...^{(1/n)}}}$
60036
How to prove this limit exists: $a_{n+2}=\sqrt{a_{n+1}}+\sqrt{a_{n}}$