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Thread: Binomial summation

  1. #1 Binomial summation 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Okay im recently in to studying series of binomial coefficients, and while i was working on it, i found this troublesome one. Perhaps any guidance or hints to the question will be great.



    Thank You


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  3. #2 Re: Binomial summation 
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    Quote Originally Posted by Heinsbergrelatz
    Okay im recently in to studying series of binomial coefficients, and while i was working on it, i found this troublesome one. Perhaps any guidance or hints to the question will be great.



    Thank You
    First, what does the n represent?


    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  4. #3 Re: Binomial summation 
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    Quote Originally Posted by Arcane_Mathematician
    Quote Originally Posted by Heinsbergrelatz
    Okay im recently in to studying series of binomial coefficients, and while i was working on it, i found this troublesome one. Perhaps any guidance or hints to the question will be great.



    Thank You
    First, what does the n represent?
    He has managed to take a very simple theorem and screw up the statement until it is unrecognizable. I had quite a long write-up describing the various possible interpretations of the theorem and why they are wrong before finally finding an inteerpretation that works. Enen then, his notation is very confusing. Unfortunately the computer burped and the simple proof was lost.

    Suffice it to say that he is looking at the alternating sum of the first n-1 binomial coefficients of an nth degree binomial. Hint: the full alternating sum os 0.

    It is not at all obvious that this is the problem under consideration.
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  5. #4 Re: Binomial summation 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by Arcane_Mathematician
    Quote Originally Posted by Heinsbergrelatz
    Okay im recently in to studying series of binomial coefficients, and while i was working on it, i found this troublesome one. Perhaps any guidance or hints to the question will be great.



    Thank You
    First, what does the n represent?
    He has managed to take a very simple theorem and screw up the statement until it is unrecognizable. I had quite a long write-up describing the various possible interpretations of the theorem and why they are wrong before finally finding an inteerpretation that works. Enen then, his notation is very confusing. Unfortunately the computer burped and the simple proof was lost.

    Suffice it to say that he is looking at the alternating sum of the first n-1 binomial coefficients of an nth degree binomial. Hint: the full alternating sum os 0.

    It is not at all obvious that this is the problem under consideration.
    Oooo this is the problem(i didnt screw anything up), and also why is this question sooo confusing too understand??, I simply didnt write the "n" in the problem posed because i was to bothered, but obviously . THe notation isnt confusing at ALL, because what my notation really says is:



    Jeez, whats the problem??... Now can i get some guides to the question, or are we just going to talk about the notation being confused and drift off the main topic again??
    ------------------




    "Mathematicians stand on each other's shoulders."- Carl Friedrich Gauss


    -------------------
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  6. #5 Re: Binomial summation 
    . DrRocket's Avatar
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    Quote Originally Posted by Heinsbergrelatz
    Quote Originally Posted by DrRocket
    Quote Originally Posted by Arcane_Mathematician
    Quote Originally Posted by Heinsbergrelatz
    Okay im recently in to studying series of binomial coefficients, and while i was working on it, i found this troublesome one. Perhaps any guidance or hints to the question will be great.



    Thank You
    First, what does the n represent?
    He has managed to take a very simple theorem and screw up the statement until it is unrecognizable. I had quite a long write-up describing the various possible interpretations of the theorem and why they are wrong before finally finding an inteerpretation that works. Enen then, his notation is very confusing. Unfortunately the computer burped and the simple proof was lost.

    Suffice it to say that he is looking at the alternating sum of the first n-1 binomial coefficients of an nth degree binomial. Hint: the full alternating sum os 0.

    It is not at all obvious that this is the problem under consideration.
    Oooo this is the problem(i didnt screw anything up), and also why is this question sooo confusing too understand??, I simply didnt write the "n" in the problem posed because i was to bothered, but obviously . THe notation isnt confusing at ALL, because what my notation really says is:



    Jeez, whats the problem??... Now can i get some guides to the question, or are we just going to talk about the notation being confused and drift off the main topic again??

    The only way to arrive at your "theorem" is to determine via divination that



    Where

    that and that






    Your theorem is then that for



    The case is simply




    So, we can make the inductive assumption and proceed













    QED
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  7. #6 Re: Binomial summation 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by Heinsbergrelatz
    Quote Originally Posted by DrRocket
    Quote Originally Posted by Arcane_Mathematician
    Quote Originally Posted by Heinsbergrelatz
    Okay im recently in to studying series of binomial coefficients, and while i was working on it, i found this troublesome one. Perhaps any guidance or hints to the question will be great.



    Thank You
    First, what does the n represent?
    He has managed to take a very simple theorem and screw up the statement until it is unrecognizable. I had quite a long write-up describing the various possible interpretations of the theorem and why they are wrong before finally finding an inteerpretation that works. Enen then, his notation is very confusing. Unfortunately the computer burped and the simple proof was lost.

    Suffice it to say that he is looking at the alternating sum of the first n-1 binomial coefficients of an nth degree binomial. Hint: the full alternating sum os 0.

    It is not at all obvious that this is the problem under consideration.
    Oooo this is the problem(i didnt screw anything up), and also why is this question sooo confusing too understand??, I simply didnt write the "n" in the problem posed because i was to bothered, but obviously . THe notation isnt confusing at ALL, because what my notation really says is:



    Jeez, whats the problem??... Now can i get some guides to the question, or are we just going to talk about the notation being confused and drift off the main topic again??

    The only way to arrive at your "theorem" is to determine via divination that



    Where

    that and that






    Your theorem is then that for



    The case is simply




    So, we can make the inductive assumption and proceed













    QED

    ThankYou for that, so hmm.... we use Mathematical induction to prove this?? say that the result wasn't given, we have no knowledge on the S_n whatsoever, and only a bunch of combinations are given like the RHS, then how would we form such result?? I was definitely thinking of the induction principle, but that method really did not satisfy me, so im still thinking real hard to arrive at such results alternate to the induction route.


    http://www.thescienceforum.com/Binom...rem-27603t.php

    you see, i have posted a similar question few months back, and i kinda got confused with some replies simply cause one of the replis says the C's aren't defined... well i think i have to make it clear, when i write . the C's are infact Well defined, as i have mentioned in my previous post. Dr.Rocket, you have suggested the induction method, and yes it works well, but i did try with integrals, and the results came out much more beautifully(IMO) BTW im talking about the other thread on the link.
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    "Mathematicians stand on each other's shoulders."- Carl Friedrich Gauss


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