1
$\begingroup$

Given $\{a_n\}_{n=1}^\infty$ bounded sequence such that $\lim_{n\to \infty} (a_{n+1}-a_n)=0$. Prove that each point in $[\liminf a_n, \limsup a_n]$ is subsequential limit of the sequence $a_n$.

1 Answers 1