Let $\{x_n\}$ be a sequence defined by $x_1 = 3, x_{n+1} = \frac{1}{4-x_n}$, for n $\geq 1$. prove it converges
62439
If $x_1 = 3$, $x_{n+1} = \frac{1}{4-x_n}$ for $n \geq 1$, prove the sequence is bounded below by $0$, above by $4$.
112510
Prove a.s. convergence of $(X_n)_n$ satisfying $E(X_{n+1} \mid F_n) \leq X_n+Y_n$ for $\sum_n Y_n<\infty$
70561
limit of the sequence $a_n=1+\frac{1}{a_{n-1}}$ and $a_1=1$
64329
Limit of the recursive sequence $a_{n+1} = \frac{1}{2}(a_n + \frac{p}{a_n})$
19159
Convergence of $\frac{1}{(\ln n)^{\ln n}}$
34025
Limit of the Sequence: $a_{n+1}=a_n+\frac{1}{a_n}$ with $a_1=1$
86970
Let $\{x_n\}$ be a sequence in a metric space such that $\{x_{2n}\}$, $\{x_{2n+1}\}$ and $\{x_{3n}\}$ all convergent. Show that $\{x_{n}\}$ converges
93022
Prove that a given recursion sequence converges
153736
Question about convergence of a simple recursive sequence
87834
How can we show that the following sequence converges?
100580
Proof that a sequence converges.
10933
Let $(x_n)$ be a bounded but not convergent sequence. Prove that $(x_n)$ has two subsequences converging to different limits.
149806
Is it possible to utilize the convergence of the sequence $z_{n+1}=a/(1+z_n)$ to prove that the sequence $x_{n+2} = \sqrt{x_{n+1} x_n}$ is convergent?
78886
Convergence of the sequence $\sqrt{1+2\sqrt{1}},\sqrt{1+2\sqrt{1+3\sqrt{1}}},\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1}}}},\cdots$
121606
How do I prove that the limit of the sequence exists: $a_n = \frac1n +\frac 1{n+1} + \frac1{n+2} + \dots + \frac1{2n}$?
53105
How to prove that this sequence converges? $\sum_{n=1}^{\infty} \frac{1}{n\ln^2(n)}$
49828
Show that the sequence $\sqrt{2},\sqrt{2\sqrt{2}},\sqrt{2\sqrt{2\sqrt{2}}},...$ converges and find its limit.