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Thread: Binomial theorem

  1. #1 Binomial theorem 
    Forum Ph.D. Heinsbergrelatz's Avatar
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    how hard do you think this question is? (not from a university student or any masters or ph.d.'s perspective)

    What is the sum to the nth term of the following?;



    apparently none of the students in out whole grade and even higher grades couldn't solve the question, surprisingly.


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  3. #2  
    Forum Junior TheDr.Spo's Avatar
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    I believe their difficulty comes from the fact that this series diverges.

    Edit: Actually, I stand to correct myself. This is an alternating harmonic series. You forgot to include the . In that case, it should converge.


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  4. #3 Re: Binomial theorem 
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    Quote Originally Posted by Heinsbergrelatz
    how hard do you think this question is? (not from a university student or any masters or ph.d.'s perspective)

    What is the sum to the nth term of the following?;



    apparently none of the students in out whole grade and even higher grades couldn't solve the question, surprisingly.
    It would help if you define the C's.
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  5. #4  
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    Quote Originally Posted by TheDr.Spo
    I believe their difficulty comes from the fact that this series diverges.

    Edit: Actually, I stand to correct myself. This is an alternating harmonic series. You forgot to include the . In that case, it should converge.
    1. It is not a harminic series.

    2. Since the numerators are a bunch of undefined C's you don't know that it is alternating.

    3. Since the numerators are a bunch of undefined C's you don't know that the nth term tends to 0 and so you don't know that the infinite series converges even if it happens to be alternating.

    4. The question was not whether the infinite series converges but instead asked for the nth partial sum.

    5. Since the numerators are a bunch of undefined C's thre nth partial sum can be ANYTHING -- see mathman's very germane comment.

    The question is impossible to answer. In fact the question, as posed, is ridiculous.
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  6. #5  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    Wait a clarification on the question, i gave the question alittle incorrectly, its not the sum we have to get, my bad. here is the actual question.


    prove the following;

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  7. #6  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Err, True

    Just define Cn as the whole thing and all the others as 0. Unless there's something else missing here, the undefined Cs could be anything.

    Edit: The title makes me think the Cs are supposed to be the combinations function, but they're missing an index/argument in that case.
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  8. #7  
    . DrRocket's Avatar
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    Quote Originally Posted by MagiMaster
    Err, True


    Edit: The title makes me think the Cs are supposed to be the combinations function, but they're missing an index/argument in that case.
    The first step in solving any problem in mathematics is a clear statement of the problem. We don't seem to have that yet.

    However, if one assumes that the C's are the binomial coefficients of order n and if the assertion is true with that assumption, then I would think that a proof by induction would be pretty straightforward (and boring).
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  9. #8  
    Forum Ph.D. Heinsbergrelatz's Avatar
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    i think i have finally proved this question i posted, but im not sure my approach is entirely correct, but it does lead to the same form as it is on the R.H.S. I would appreciate any corrections if there are any mistakes.

    first of all i tried to write this question in terms of an integral, this way the C's do not necessarily have to be defined;



    now all i have to do is solve this simple yet puzzling integral; so by substituting







    now solving this integration by parts you get;








    so on and on... till eventually it becomes;



    and through another integral we can calculate that

    thus the final proof is complete;

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