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Math Help - proof of a theorem

  1. #1
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    Question proof of a theorem

    Theorem states:
    Note that a (sub n) is a constant sequence.
    Suppose a (sub n) = a for all n greater than or equal to 1.
    Then lim a (sub n) as n approaches infinity = a.

    I need to prove this.
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  2. #2
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    Quote Originally Posted by Carol View Post
    Theorem states:
    Note that a (sub n) is a constant sequence.
    Suppose a (sub n) = a for all n greater than or equal to 1.
    Then lim a (sub n) as n approaches infinity = a.

    I need to prove this.
    Is it true that |a_n - a|<\epsilon?
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Carol View Post
    Theorem states:
    Note that a (sub n) is a constant sequence.
    Suppose a (sub n) = a for all n greater than or equal to 1.
    Then lim a (sub n) as n approaches infinity = a.

    I need to prove this.
    you need to use the definition of the limit for a sequence to show that \lim_{n \to \infty}a_n = a

    that is, you must show that: for every \epsilon > 0, there exists an N \in \mathbb{N} such that n > N implies |a_n - a|< \epsilon
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