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Math Help - Series Expansion

  1. #1
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    Series Expansion

    What is the coefficient of in the power series expansion of ?

    I'm having trouble expanding this. Could someone explain how to solve it? Cheers.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Haris View Post
    What is the coefficient of in the power series expansion of ?

    I'm having trouble expanding this. Could someone explain how to solve it? Cheers.
    you don't need to expand anything

    let f(x) = \frac 1{(9 + 5x)^{1/4}}

    the coefficient of the x^2-term is given by

    \frac {f''(0)}{2!}
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  3. #3
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    Quote Originally Posted by Haris View Post
    What is the coefficient of in the power series expansion of ?

    I'm having trouble expanding this. Could someone explain how to solve it?
    Write it as 9^{-1/4}\bigl(1+\tfrac{5x}9\bigr)^{-1/4}. Then use the binomial expansion of (1+t)^{-1/4}, taking t=5x/9.

    Edit. Alternatively, use Jhevon's method. It's equally good.
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