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OT math help.

Discussion in 'Electronic Basics' started by George Herold, Dec 18, 2013.

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  1. Hi all, I was helping my daughter with algebra last night.
    One set of problems had you find the generating function for a list of integers.
    For instance,
    list was 1,4,16,64...
    Which I wrote as F(n) = 4*F(n-1), F(1) = 1
    The HW started counting at n=1 rather than zero... but that hardly matters.
    Now my way to solve this is just to guess at the answer. (not very helpful to my daughter.) So I had her play around with different guesses till we 'found' the answer.
    F(n) = 4^(n-1).
    But it seems there should be a more formal way to arrive at the answer.
    So what is it?
    A solution for the above would be fine... or web link, or just tell me what this type of problem is called and I can go find the answer on my own.

    Thanks George (and Elsie) H.
     
  2. Thanks Jim, that helps. After posting the question I went and 'guessed' a solution but with unknown coefficients, and then plugged the guess back into the
    formula and 'found' the coef. So that at least works. The math 'savy' comes in making a good guess!

    Is it correct to think of these types of problems as a 'digital' form of a differential equation?

    George H.
     
  3. Phil, do you every get the feeling that you're too smart for your own good?
    (He asked with a smile on his face.)

    Did you miss the three little dots? 16,64... so 256, 1024... (etc.)

    So given F(n) = 4*F(n-1) and F(1) = 1, is making a good guess the best way to get to a solution? (with unknown coefficients.)

    George H.
     
  4. Fun, I never heard of pedagogue. Hmm if I tell her math teacher I hear she's a good pedagogue will I be slapped?
     
  5. Jasen Betts

    Jasen Betts Guest


    The "easy" way to automate it is to find a polynomial
    solution by means on simultaneousl equations.

    That won't find 4^(n-1) but something else that fits those points.



    the other way is to type them into google, with quotes around them
    you'll get a result from OEIS

    I remeber being given sequences like this 4,3,3,5,4,4,3,5,5,4,3,6,6,8
    or 7,8,4,5,3,4,4 in highschool.. I suspect these where put on the end keep the
    fast students quiet.
     
  6. Feeling chastised.
    Lowers head, kicks dirt with shoe, "Sorry guys".

    (I just hope they don't see the little smirk on my face :^)

    George H.
     
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