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Math Help - Summation notation

  1. #1
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    Summation notation

    I don't know how to write the symbol sigma on here but the lower limit is 1 and the upper limit is 4 and (xi - yi)^2. I need the method on how to do it.
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  2. #2
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    Quote Originally Posted by marie7 View Post
    I don't know how to write the symbol sigma on here but the lower limit is 1 and the upper limit is 4 and (xi - yi)^2. I need the method on how to do it.
    First of all, we need to be clear on what the problem is. Do you mean:

    \sum^4_{i=1}(xi-yi)^2?
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  3. #3
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    yes that's correct sorry I don't know how to do the symbols
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    Quote Originally Posted by marie7 View Post
    yes that's correct sorry I don't know how to do the symbols
    OK... well this is sort of an odd sum. The x and y aren't involved in the indexing, so we can take them out. We get

    (x-y)^2\sum_{i=1}^4 i^2.

    Now the sum should be very simple to solve.
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  5. #5
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    Quote Originally Posted by AlephZero View Post
    OK... well this is sort of an odd sum. The x and y aren't involved in the indexing, so we can take them out. We get

    (x-y)^2\sum_{i=1}^4 i^2.

    Now the sum should be very simple to solve.
    Well the x and y have number values and I just wanted the method so I could do it myself but here are the numbers:
    for x1 = 2, x2 = -3, x3 = 10 x4 = -5, x5 = -3
    for y1 = -1, y2 = 3, y3 = 5, y4 = 7, y5 = -2.

    i is supposed to represent for example 1 in x1, 2 in x2 etc. Its a little i.
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  6. #6
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    Quote Originally Posted by marie7 View Post
    Well the x and y have number values and I just wanted the method so I could do it myself but here are the numbers:
    for x1 = 2, x2 = -3, x3 = 10 x4 = -5, x5 = -3
    for y1 = -1, y2 = 3, y3 = 5, y4 = 7, y5 = -2.

    i is supposed to represent for example 1 in x1, 2 in x2 etc. Its a little i.
    Alright, so when I asked you previously if I had typed up the problem correctly, and you said "yes," that wasn't true, evidently. And you are now providing, in addition, a hugely crucial portion of the problem that you also neglected to mention.

    So now I ask you again. Think very hard. Is this the problem:

    \sum_{i=1}^4 (x_i - y_i)^2?
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  7. #7
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    yeah it is.
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  8. #8
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    Well, then the easiest way to do it is just expand the sum, and substitute the values:

    \sum_{i=1}^4(x_i-y_i)^2 = (x_1-y_1)^2 + (x_2-y_2)^2+(x_3-y_3)^2+(x_4-y_4)^2.

    Simply plug in the values and do the arithmetic.
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  9. #9
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    I got -146 as my answer, is that correct?
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  10. #10
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    No, Marie. 'fraid not.

    Hint:

    Spoiler:
    Your answer cannot be negative because you're taking the same of "squares". Can A squared number be negative?
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  11. #11
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    I plugged the numbers in like this (2 -(-1))^2 + (-3-3)^2 + (10 - 5)^2 + (-5-7)^2

    Am I right?
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  12. #12
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    Quote Originally Posted by marie7 View Post
    I got -146 as my answer, is that correct?
    Ah, no, I'm afraid not, for at least 3 reasons. First, I have done the arithmetic myself based on the numbers you provided, and reached a different solution. Second, your answer is a negative number, and since the expression at hand involves the sum of four squares, a negative answer is impossible. Thirdly, you have provided a question involving a finite sum with 4 terms, and supplied data for 5 terms, so something is bound to be wrong with just about any answer you come up with.
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  13. #13
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    yes but the upper limit is four so I only do from 1 to four not 1 to five, does that make sense?
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  14. #14
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by marie7 View Post
    I plugged the numbers in like this (2 -(-1))^2 + (-3-3)^2 + (10 - 5)^2 + (-5-7)^2

    Am I right?
    You plugged 'em in right, but unfortunately arrived at the wrong answer. What did you do after that?

    Look at my last post for a hint.
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  15. #15
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by marie7 View Post
    yes but the upper limit is four so I only do from 1 to four not 1 to five, does that make sense?
    Correct!
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