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Math Help - Summations

  1. #1
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    Summations

    Find the sum when n=1000. Show all your steps. Use the properties of summation.

    i=1 -->n ((4i/n^2)+(i^3/n))*(6/i)

    Thank you very much....I hope I hear back asap!!!
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  2. #2
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    You're performing this sum, then?

    \displaystyle\sum_{i=1}^{n}\left[\left(\frac{4i}{n^{2}}+\frac{i^{3}}{n}\right)\frac  {6}{i}\right]?

    If so, I would note two things:

    1. You can simplify a bit before summing.
    2. It's true from principles of induction that

    \displaystyle\sum_{i=1}^{n}i^{2}=\frac{n(n+1)(2n+1  )}{6}.

    So what does that tell you?
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  3. #3
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    Thank you

    Thank you so much...you saved me!!!!
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  4. #4
    A Plied Mathematician
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    You're welcome. You have solved it, then?
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  5. #5
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    No I did not sadly, and it is due in one hour. Can you direct me anymore?
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  6. #6
    A Plied Mathematician
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    If it's "due", then it is for a grade, right? Forum policy is not knowingly to help with graded problems.
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  7. #7
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    "Due" was not the right word. Sorry this is the first time I have used this site. It is a practice problem given before our classes. My apologies, thanks for that information. Not for a grade.
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  8. #8
    A Plied Mathematician
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    Well, what simplifications do you get?
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