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Thread: Finding terms with given binomial?? Binomial Theorem?

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    Finding terms with given binomial?? Binomial Theorem?

    Hi, I forgot how to plug in the binomial Theorem.

    My two problems:

    1) Find the 5th term of the given binomial. (a+ square root of (b))^9

    2) Find the 6th term of the given binomial (p/2-q/2)^9
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    Re: Finding terms with given binomial?? Binomial Theorem?

    $(a+b)^n = \displaystyle{\sum_{k=0}^n}\begin{pmatrix}n \\ k\end{pmatrix}a^k b^{n-k}$
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    Re: Finding terms with given binomial?? Binomial Theorem?

    Quote Originally Posted by math951 View Post
    My two problems:
    1) Find the 5th term of the given binomial. (a+ square root of (b))^9
    2) Find the 6th term of the given binomial (p/2-q/2)^9
    I and most who have done work for the testing community will not answer these.
    The fact is there is no one correct answer.

    In the expansion ${(a + b)^9} =\displaystyle \sum\limits_{k = 0}^9 {\dbinom{9}{k}{a^k}{b^{9 - k}}}$ has ten terms.
    BUT the expansion ${(a + b)^9} =\displaystyle \sum\limits_{k = 0}^9 {\dbinom{9}{k}{a^{9-k}}{b^{k}}}$ is the equivlant expansion, just in a different order.
    The sixth term in the first first expansion which is not the sixth term in the second expansion.
    So which is the sixth term in $(a+b)^9~?$

    You may show your teacher this if you like.
    Thanks from topsquark, HallsofIvy and bigwave
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