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Math Help - Extremely Urgent!

  1. #1
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    Exclamation Extremely Urgent!

    I have four values, and I have to put them in summation notation. It would be appreciated if someone could help me, thanks!

    0.00391
    0.0352
    0.00977
    0.191

    I guess it would help converting them into fractions at first, but I don't seem to know where to move on from there because I can't seem to find a pattern between the four values. Your help would greatly be appreciated.

    Thanks,
    Sam
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  2. #2
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    Quote Originally Posted by samantha_malone View Post
    I have four values, and I have to put them in summation notation. It would be appreciated if someone could help me, thanks!

    0.00391
    0.0352
    0.00977
    0.191

    I guess it would help converting them into fractions at first, but I don't seem to know where to move on from there because I can't seem to find a pattern between the four values. Your help would greatly be appreciated.

    Thanks,
    Sam
    Hi samantha,

    Do you mean 0.00391+0.0352+0.00977+0.191?

    I think there are many ways you could do this, but the easy way out is to use a cubic polynomial, i.e.

    \sum_{x=1}^4 (ax^3+bx^2+cx+d)

    Why? Because we have four values, we can create four equations, and since a cubic polynomial has four unknowns, we can solve for them, integrating our values into the sum... it's hard to explain, but easier if we just do it!

    Let f(x)=ax^3+bx^2+cx+d

    Then, for instance,

    f(1)=0.00391

    f(2)=0.0352

    f(3)=0.00977

    f(4)=0.191

    Solving either using a calculator or by hand (), we get

    (a,b,c,d)=\left(\frac{13169}{300000}, -\frac{14587}{50000}, \frac{17977}{30000}, -\frac{8687}{25000}\right)

    So the summation is

    \sum_{x=1}^4 \left(\frac{13169}{300000}x^3-\frac{14587}{50000}x^2+\frac{17977}{30000}x-\frac{8687}{25000}\right)
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