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Thread: Can you solve this?

  1. #1
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    Can you solve this?

    Posted this in the Extracurricular Secondary Maths thread, only to realise it was Secondary Maths . Re-posting here:

    Define X(n) & Y(n) in the following manner:

    X(1) = Y(1) = 1, otherwise:

    X(n)
    = 2X(n-1) if n is Even
    = 2X(n-1) - 1 if n is Odd


    Y(n)
    = 2Y(n-1) + 1 if n is Even
    = 2Y(n-1) if n is Odd

    Examples:

    X(n) | 1 | 2 | 3 | 6 | 11 | 22 | 43 | 86 | ...
    Y(n) | 1 | 3 | 6 | 13 | 26 | 53 | 106 | 213 | ...
    n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ...

    The problem:

    Find Y(n)/X(n) as n -> infinity.

    Good luck
    Last edited by Mikamesh; 19 Jul 2016 at 8:05 PM.

  2. #2
    Supreme Member seanieg89's Avatar
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    Re: Can you solve this?

    I think 5/2, will write proof in a sec.

    Last edited by seanieg89; 19 Jul 2016 at 9:00 PM.
    Mikamesh likes this.

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