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Math Help - A recursive relation table and proving problem...

  1. #1
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    A recursive relation table and proving problem...

    Hello

    Given this:
    an = a(n-1) - 1/4A(n-2)
    Where n is an element of N (any whole number, 0,1,2,3...)

    a1 = a2 = 1


    Create a table with A1, A2, A3, A4, A5 and their answers.

    Then prove that the explicit formula is:
    An = n(1/2)^n-1

    My shot at it:
    The thing that I am stumped on:
    a1 = a2 = 1
    Does this mean that for all N's the answer is 1?
    a3 = a(n-1) - 1/4A(n-2)
    a3 = a2 - 1/4*a1, a3 = 1 - 1/4*1 = 0.25???
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  2. #2
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    a3 = a2 - 1/4*a1, a3 = 1 - 1/4*1 = 0.25???
    Correct, (ignoring that you put a 0.25 instead of 1 0.75)
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  3. #3
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    The prize for doing math at 6 am after a night in the C++ language.
    1-0.25 = 0.75!

    Thanks a ton, but how do I prove or not prove that the formula can be written as:
    An = n(1/2)^n-1?

    I mean, doing so leaves me with the same answers... so the formula is correct, but proving it???
    Of course I could write it with words, explaninig why, but that does not prove it? hmm...
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  4. #4
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    Just show that that formula satisfies the given recursive relation. If it has the correct values at n= 1 and 2 and satisfies the relation, then it is a correct solution. That's what "solution" means!
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  5. #5
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    Alright, consider it done!
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