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Math Help - Sequence and limit point

  1. #1
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    Sequence and limit point

    Hi, I need help on the following:

    Let  A = \{\frac{m}{2^n} \} where m,n are integers.  \frac{1}{3} is given as a limit point of A. Find a sequence in A that converges to  \frac{1}{3}

    Thanks
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by RB06 View Post
    Hi, I need help on the following:

    Let  A = \{\frac{m}{2^n} \} where m,n are integers.  \frac{1}{3} is given as a limit point of A. Find a sequence in A that converges to  \frac{1}{3}

    Thanks
    What about a_n := \frac{m}{2^n}, where m := \lceil \frac{2^n}{3}\rceil?
    Because then you get that a_n \in A , I think, and that

    \frac{1}{3}\leftarrow \frac{\frac{2^n}{3}-1}{2^n} \leq a_n = \frac{\lceil \frac{2^n}{3}\rceil}{2^n} \leq \frac{\frac{2^n}{3}+1}{2^n}\rightarrow \frac{1}{3}
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