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Math Help - Limited Sequence?

  1. #1
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    Limited Sequence?

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

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Wright View Post
    Hello again.
    How do you check if a sequence is limited. Sequence, not series! :P

    Thanks in advance.
    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}^+
    Last edited by Defunkt; November 5th 2009 at 09:21 AM.
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