Show that $\sqrt{2+\sqrt{2+\sqrt{2...}}}$ converges to 2
686
$\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
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
76050
Test for convergence of the series $\sum_{n=1}^{\infty}\frac{n}{\sqrt{n^2 +1}}$
19174
Definition of convergence of a nested radical $\sqrt{a_1 + \sqrt{a_2 + \sqrt{a_3 + \sqrt{a_4+\cdots}}}}$?
17902
Prove or disprove: $\sum a_n$ convergent, where $a_n=2\sqrt{n}-\sqrt{n-1}-\sqrt{n+1}$.
35929
Convergence of series $\sum_{n=1}^{\infty}{\frac{1}{\sqrt{1}+\sqrt{2}+...+\sqrt{n}}}$
62485
How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
125340
Prove the convergence of a series.
114141
If $\sum a_n^2 n^2$ converges then $\sum |a_n|$ converges
76867
Does $\sum _{k=2} ^\infty \frac{(-1)^k}{\sqrt{k}+(-1)^k}$ converge conditionally?
32436
Convergence of $\sum _{k=1}^\infty \sin \left(\sqrt{k}\right)/k$
82562
Prove that $\sum_{n=2}^\infty (\ln n)^{- \ln n}$ converges
49860
Determine the convergence of $\sum\limits_{n=2}^\infty \frac{\sqrt{n+1}}{n(n-1)}$
89373
Convergence of $\frac{\sqrt{a_{n}}}{n}$
129823
Show that $\sum_{n=1}^{\infty}(n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+\frac{1}{6})$ converges
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
87834
How can we show that the following sequence converges?