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Math Help - A convergent sequence problem

  1. #1
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    A convergent sequence problem

    Q: Let the sequence {An} converge to a with a>0, prove there exist an N within the set of natural numbers such that n >= N implies {An} > 0

    thank you!
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  2. #2
    TD!
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    The convergence of the sequence (A(n)) to a tells you that for all e > 0, there exists an N such that for all n > N, |A(n)-a| < e.

    This last statement is equivalent to saying that a-e < A(n) < a+e, but you know that a > 0.

    Now just take the e > 0 small enough such that a > e which implies a-e > 0 and thus A(n) > 0.
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  3. #3
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    Using what TD has shown you, I would suggest e = \frac{a}{2}.
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  4. #4
    TD!
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    I was hoping tttcomrader would be figuring out that himself
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