# Math Help - Limited Sequence?

1. ## Limited Sequence?

Hello again.
How do you check if a sequence is limited. Sequence, not series! :P

If you mean convergent, then a sequence $\{a_n\}_{n=1}^{\infty}$ converges to a limit L, by definition, if for any $\epsilon > 0$, there exists some $N(\epsilon) \in \mathbb{N}$ such that for any $n\geq N(\epsilon), \ |a_n-L|<\epsilon$
If you mean bounded, then a sequence $\{a_n\}_{n=1}^{\infty}$ is bounded if $\forall n\in \mathbb{N}, \ |a_n| \leq M$ for some $M \in \mathbb{R}^+$