I want an example of a sequence that satisfies $\mid x(n) - x(n-1)\mid \to 0$ but not Cauchy
59584
A sequence of real numbers such that $\lim_{n\to+\infty}|x_n-x_{n+1}|=0$ but it is not Cauchy
143424
Sequence problem involving inequalities
117179
Show that a Cauchy sequence has a fast-Cauchy subsequence
51223
Example of decreasing sequence of sets with first set having infinite measure
8151
Example to the statement that $a_{n+1} - a_n \rightarrow 0$ as $n \rightarrow \infty$ does not imply that sequence $a_n$ converges.
37906
Prove $s_n$ is a Cauchy sequence for $|s_{n+1}-s_n|\lt2^{-n}$
147841
Please help prove that $(x_n)$ is a Cauchy sequence if $|x_{n+1} - x_n| \leq Cr^n$
94397
Example of a non-splitting exact sequence $0 → M → M\oplus N → N → 0$
90074
Show that the sequence $1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,2,0,2,1,\cdots$ isn't periodic
8814
Proving that a sequence such that $|a_{n+1} - a_n| \le 2^{-n}$ is Cauchy
141895
Proving that a sequence is monotone
106960
Proof to sequences in real analysis
2092
Convergence of a sequence with assumption that exponential subsequences converge?
20136
Convergence of the sequence $ \sqrt {n-2\sqrt n} - \sqrt n $
11586
Sequences of Real Numbers in a closed bounded interval
31930
Given the sequence $(x_n)$ is unbounded, show that there exist a subsequence $(x_{n_k})$ such that $\lim(1/x_n)=0$.
29138
If $\{x_n\}$ satisfies that $x_{n+1} - x_n$ goes to $0$, is $\{x_n\}$ a Cauchy sequence?