find a sequence of rational numbers such that: $\lim_{n \to \infty} x_n = x_0 $ when $x_0$ is irrational
40719
Give a concrete sequence of rationals which converges to an irrational number and vice versa.
7815
Prove that $\lim_{n\to\infty}a_n^2=a^2$ when ${a_n}$ is a sequence in $\mathbb{R}$ with $\lim_{n\to\infty}a_n=a$
59584
A sequence of real numbers such that $\lim_{n\to+\infty}|x_n-x_{n+1}|=0$ but it is not Cauchy
138977
Infinitely many rational numbers between two different real numbers
81052
Determining a limit of parametrized, recursively defined sequence $a_{n+1}=1+\frac{(a_n-1)^2}{17}$
87116
Prove $ \lim_{n\to \infty}\frac{n}{n+1} = 1$ using Cauchy (epsilon) definition of a limit of a sequence
133886
Existence of increasing sequence $\{x_n\}\subset S$ with $\lim_{n\to\infty}x_n=\sup S$
154578
Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
5728
How to prove $\lim_{n \to \infty} \sqrt{n}(\sqrt[n]{n} - 1) = 0$?
45885
If there exist sequence such that $g(x_n)=f(x_{n+1})$, then we have $g(x_0)=f(x_0)$ for some $x_0$
146826
Fibonacci Sequence and series limits
66441
Prove that $|x|<1$ implies that $\lim_{n \to \infty} x^n=0$
12031
Asymptotic behavior of the sequence $a_n=\sqrt{n+a_{n-1}}$
86319
Give an example of a bounded, non-convergent real sequence $(a_n)$ s.t. $a_n-a_{n-1}\rightarrow 0$
61361
Find the set of $x>0$ such that the series $\sum\limits_n x^{\ln{n}}$ converges
9781
How to prove that $\lim_{n \to \infty} n x^{n} = 0 $ when $0<x<1$?
58985
Does an increasing sequence of reals converge if the difference of consecutive terms approaches zero?