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Math Help - terms and others

  1. #1
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    terms and others

    (2x^2 - 3/x)^18

    how can I find the 16th term and follow up by finding the term that is independent of x?
    Last edited by Stuart; May 15th 2006 at 04:02 PM.
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  2. #2
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    Quote Originally Posted by Stuart
    (2x^2 - 3/x)^18

    how can I find the 16th term and follow up by finding the term that is independent of x?
    The 16th term of (a+b)^{18} is,
    {18 \choose 15}a^{15}b^3
    Over here a=2x^2,b=-3/x
    Thus,
    {18 \choose 15}(2x^2)^{15}(-3/x)^3=-816(2^{15}x^{30})\cdot \frac{3^3}{x^3}=-815\cdot 2^{15} \cdot 3^3\cdot x^{27}
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  3. #3
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    Ok well I am sure that K = 12 and N = 18

    so to set it up is 18c12 * (2x^2)^18-12 * (-3/x)^12

    Right and follow through with that you gave for the 16th term? If not what does the 18 over 15 mean?
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  4. #4
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    Quote Originally Posted by Stuart
    Ok well I am sure that K = 12 and N = 18

    so to set it up is 18c12 * (2x^2)^18-12 * (-3/x)^12

    Right and follow through with that you gave for the 16th term? If not what does the 18 over 15 mean?
    It is another way of writing 18C15
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