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Math Help - Calculate the coefficient of a given term in a power series

  1. #1
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    Calculate the coefficient of a given term in a power series

    Hello.

    I don't know how to calculate given coefficients in a given series. For example

    (x^{3}+x^4+x^5+...)
    coefficient next to x^{13}=?

    or a different one:

    (2+3x)^3 \sqrt{2+x}
    coefficient next to x^5=?

    Could you explain to me how it is done?
    Last edited by wilhelm; November 26th 2012 at 11:20 AM.
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  2. #2
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    Re: Calculate the coefficient of a given term in a power series

    Quote Originally Posted by wilhelm View Post
    I don't know how to calculate given coefficients in a given series. For example
    (x^{3}+x^4+x^5+...)|| coefficient next to x^{13}=?

    or a different one:
    (2+3x)^3 \sqrt{2+x}|| coefficient next to x^5=?

    You must define the terms and the notation.

    I dare say that most of us have never seen (x^{3}+x^4+x^5+...)|| before.

    What does the || signify?
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  3. #3
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    Re: Calculate the coefficient of a given term in a power series

    I'm sorry, it doesn't signify anything. I don't know why I put it there. It is simply a series (x^3+x^4+...)^3. Is it all right now?
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  4. #4
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    Re: Calculate the coefficient of a given term in a power series

    Quote Originally Posted by wilhelm View Post
    I'm sorry, it doesn't signify anything. I don't know why I put it there. It is simply a series (x^3+x^4+...)^3. Is it all right now?
    You need to find text material of generating functions.

    There is a good free pdf generatingfunctionology on the web.
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  5. #5
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    Re: Calculate the coefficient of a given term in a power series

    (x^3 + x^4 + ...) = x^9(1+x+x^2+...) = x^9/(1-x)^3. You can expand the denominator and use a Taylor series expansion and collect the coefficients.
    You can try looking up Maclaurin series or Taylor series expansion.
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