Show that the sequence $x_{n+1}=1+\sqrt {x_n}$ is convergent
67535
Limit of a difference equation
85217
Boundedness and convergence of $x_{n+1} = x_n ^2-x_n +1$
151593
Prove that the limit of $\sqrt{n+1}-\sqrt{n}$ is zero
8715
Let $(a_n)_n$ be a convergent sequence of integers , what can we say about $(a_n)_n$
153121
show that $\{x_n\}$ is a cauchy sequence
74522
Convergence of a sequence, $a_n=\sum_1^nn/(n^2+k)$
144786
Show that the following inductively defined sequence converges and find its limit.
33965
Convergence of $\sum_{n=1}^\infty (-1)^n(\sqrt{n+1}-\sqrt n)$
145863
sequence of positive numbers satisfying $a_{n+1}=\frac{2}{a_n+a_{n-1}}$, prove it converges
42300
Let the sequence be defined recursively $X_{n+1}=pX_{n}+q$ for p nonzero and $X_{1}$ arbitrary. In what conditions does the sequence converge?
15319
Convergence of recurrence sequence
35885
Monotonicity and convergence of the sequence $a_n=\sum_{k=1}^{n}\frac{1}{k+n}$
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.
57095
How do I prove the sequence $x_{n+1}=\sqrt{\alpha +x_n}$, with $x_0=\sqrt \alpha$ converges? ( boundedness?)
38002
how to prove that this positive sequence converges to 1
114665
Show the series $a_n/(1+a_n)$ converges absolutely
100580
Proof that a sequence converges.