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Math Help - Binomial Series

  1. #1
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    Binomial Series

    Use the binomial series to get a 3 term series for (2+4rootx)^3 and find the valid values for x.

    What do u do with the 2?
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  2. #2
    Super Member Deadstar's Avatar
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    Ok. You gotta change it to the form (1+x)^n so...

    (2 + 4 \sqrt{x})^2 = (2(1 + 2\sqrt{x}))^3 = 2^3 (1+2\sqrt{x})^3

    Then plug this into the binomial series which is...

    (1+x)^n = 1 + nx + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3 + \dots

    With n=3 and x=2\sqrt{x}.

    The binomial series is valid when |x|<1 so find x such that |2\sqrt{x}|<1
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  3. #3
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    Thanks ALOT, sorry for late reply...
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