Let $\{ a_{n}\}$ be a positive real sequence $a_{n}=\sqrt{a_{n-1}a_{n-2}}$ for $n≥3$, then $\{ a_{n}\}$ converges to $(a_{1}a_{2}^{2})^{1/3}$.
29266
Limit of a sequence defined by recursive relation : $ a_n = \sqrt{a_{n-1}a_{n-2}}$
5797
Limit of the sequence $a_n=\sqrt[n+1]{(n+1)!}-\sqrt[n]{n!}$
8715
Let $(a_n)_n$ be a convergent sequence of integers , what can we say about $(a_n)_n$
142
Showing the sequence converges to the square root
132140
Convergence of Sequence of Real Numbers
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.
9134
Suppose $\sum{a_n}$ converges. How do I prove that $\sum{\frac{\sqrt{a_n}}{n}}$ converges
20136
Convergence of the sequence $ \sqrt {n-2\sqrt n} - \sqrt n $
107399
A sequence and convergence
19225
Let $\{a_n\}$ be defined as follows: $a_1 = 2$, $a_{n+1}=\frac{1}{3-a_n}$, if $n \geq 1$. Does $\{a_n\}$ converge?
140220
Convergence of $\sum_{n=2}^{\infty}\frac{\sqrt{a_{n}}}{\ln\, n}(n^{a_{n}}-1)$
17902
Prove or disprove: $\sum a_n$ convergent, where $a_n=2\sqrt{n}-\sqrt{n-1}-\sqrt{n+1}$.
17231
How I can prove that the sequence $\sqrt{2} , \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}$ converges to 2?
144786
Show that the following inductively defined sequence converges and find its limit.
65592
Convergence of $a_n=(1/2)^{(1/3)^{...^{(1/n)}}}$
135018
Proving that a sequence has $a_n = a_{n+2}$ for $n$ sufficiently large.
42567
Let $(a_n)_{n \geq 0}$ be a strictly decreasing sequence of positive real numbers , and let $z \in \mathbb C$ , $|z| < 1$.