Convergence of the sequence $\sqrt{1+2\sqrt{1}},\sqrt{1+2\sqrt{1+3\sqrt{1}}},\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1}}}},\cdots$
13617
Evaluating the nested radical $ \sqrt{1 + 2 \sqrt{1 + 3 \sqrt{1 + \cdots}}} $.
123942
Prove $\frac{1}{2}\sum_p \frac{1}{p^2}+\frac{1}{3}\sum_p \frac{1}{p^3}+\cdots$ converges
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
27068
Show that $\sqrt{2+\sqrt{2+\sqrt{2...}}}$ converges to 2
88365
Prove the sequence converge and find its limit
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.
105971
Convergence of $\sum \limits_{n=1}^{\infty}\sqrt{n^3+1}-\sqrt{n^3-1}$
50087
Convergence of $a_{n+1}=\frac{1}{1+a_n}$
13701
Prove convergence of the sequence $(z_1+z_2+\cdots + z_n)/n$ of Cesaro means
145863
sequence of positive numbers satisfying $a_{n+1}=\frac{2}{a_n+a_{n-1}}$, prove it converges
46685
Show that the sequence $a_1=1$, $a_2=2$, $a_{n+2} = (a_{n+1}+a_n)/2$ converges by showing it is Cauchy
35885
Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
148492
Finding the limit of the sequence $(1 - 1/\sqrt 2) \dotsm ( 1 - 1/\sqrt {n+1})$
93022
Prove that a given recursion sequence converges
107311
Convergence of a sequence and some of its subsequences
48500
Proof of convergence of sequences
35929
Convergence of series $\sum_{n=1}^{\infty}{\frac{1}{\sqrt{1}+\sqrt{2}+...+\sqrt{n}}}$