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Math Help - result

  1. #1
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    result

    calculate result (clueless)



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  2. #2
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    Re: result

    Quote Originally Posted by Petrus View Post
    calculate result
    Here it is done.
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  3. #3
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    Re: result

    any possible i can get a smal step by step because i havent really understand this method ( pretty new on it )
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  4. #4
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    Re: result

    Why clueless? Do you not know what \begin{pmatrix}22 \\ i \end{pmatrix} means? It is the "binomial coefficient" \begin{pmatrix}n \\ i\end{pmatrix}= \frac{n!}{i!(n- i)!}.

    If you do know that, then this can be done by simple arithmetic:
    \begin{pmatrix}22 \\ 1\end{pmatrix}+ 2\begin{pmatrix}22\\ 2\end{pmatrix}+ \cdot\cdot\cdot+ 21\begin{pmatrix}22 \\ 21\end{pmatrix}+ 22\begin{pmatrix}22 \\ 22\end{pmatrix}
    = 1+ 2(22)+ \cdot\cdot\cdot+ 21(22)+ 22
    Tedious, but just arithmetic. (I will admit that " \cdot\cdot\cdot" hides some pretty big numbers!)

    But if you are clever, you will remember that "binomial coefficients" are so named because (x+ 1)^n= \sum_{i=0}^\infty \begin{pmatrix}n \\ i\end{pmatrix}x^i so that, if you take x= 1, (1+ 1)^n= 2^n= \sum_{i=0}^\infty\begin{pmatrix}n \\ i\end{pmatrix}.

    What about that "p" multiplying the binomial coefficient? Think about the derivative of (x+ 1)^n= \sum_{i=0}^\infty \begin{pmatrix}n \\ i\end{pmatrix}x^i with respect to x.
    Last edited by HallsofIvy; October 27th 2012 at 01:27 PM.
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  5. #5
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    Re: result

    Quote Originally Posted by Petrus View Post
    any possible i can get a smal step by step because i havent really understand this method
    Well I doubt it.
    But here is an example. Say p=10 then 10\cdot\binom{22}{10}=10\frac{22!}{(10!)(12!)}~.

    You have to do that 22 times, then add it up.
    Last edited by Plato; October 27th 2012 at 01:28 PM.
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    Re: result

    Its just that i cant sit do this all in a test... if this would be on a test how do u think i can answer this problem?
    edit: with none calculate ^^
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    Re: result

    So- you are expected to know the binomial theorem.
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    Re: result

    One last question when u rewrite it in 1+2(22)+3(22) i actually did not se where 1 comes from but rest i did get it can u explain?
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  9. #9
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    Re: result

    Quote Originally Posted by HallsofIvy View Post
    ...Think about the derivative of (x+ 1)^n= \sum_{i=0}^\infty \begin{pmatrix}n \\ i\end{pmatrix}x^i with respect to x.
    This is the ticket right here.
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  10. #10
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    Re: result

    Quote Originally Posted by Petrus View Post
    calculate
    Here is a comment about the thread and where it was posted.
    It is posted in Pre-University algebra forum..
    That has to be in most elementary forum on the entire board.
    Therefore, I try to answer in that sprite.
    If Petrus expects a high level answer then questions should be posted in an more appropriate forum.
    I do not think the answer \sum\limits_{k = 1}^N {k\binom{N}{k}}  = N \cdot 2^{N - 1} is appropriate for this forum.
    Even if it is a well-known fact.
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  11. #11
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    Re: result

    Quote Originally Posted by Plato View Post
    ...questions should be posted in an more appropriate forum...
    I agree completely. Your conscientious suggestion is exactly what would be expected for a pre-calculus student.

    I happen to know from corresponding with the OP that he is in a course involving the calculus.
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