If sequence $x_n$ converges to $x$, prove that $\sqrt x_n$ converges to $\sqrt x$
108429
Show that if $x_n \to x$ then $\sqrt{x_n} \to \sqrt{x}$
55464
Convergence of sequence given by $x_1=1$ and $x_{n+1}=x_n+\sqrt{x_n^2+1}$
112430
Prove that sequence $ x_{(n+1)}= \frac {a}{1+x_n}$ is convergent to positive root of $x^2+x-a=0,$where $a >0$ and $x_1 >0$
52711
Prove that the sequence $\{v_n\}$ converges to the maximum value of $f$ on $[a,b]$
129351
Show that $\sqrt{n^2+1}-n$ converges to 0
70746
Proving that $(x_n)_{n=1}^{\infty}$ is a Cauchy sequence.
142
Showing the sequence converges to the square root
107311
Convergence of a sequence and some of its subsequences
55340
Prove that $r^n/n!$ converges where $n\ge r$
125925
Convergence of $f_n(x)=x^n(1-x)^n$
100580
Proof that a sequence converges.
100234
Proving that $x^n$ converges to $0$ whenever $|x| < 1$
65833
Proving a sequence converges by defining the sequence recursively.
30167
Convergence of $\sqrt[n]{x^n+y^n}$ (for $x, y > 0$)
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.
157847
If $x_n \to 0$, show that $\sqrt{x_n} \to 0$
107735
What does the following sequence converge to?