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Math Help - Not sure what kind of maths but I think its summination

  1. #1
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    Not sure what kind of maths but I think its summination

    Hey also dont know if this is the right section of the forum but I guess an admin can move it and tell me where it is.



    If you look at the nth formula for these you can see it is squared in the 2nd formula. I don't think its a random occurrence and my maths teacher also doesn't know why its like that. Do any of you and can you prove why?
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  2. #2
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    Hello, Dark Ainur!


    \sum^n_{i=1}i \;= \;1 + 2 + 3 + \cdots + n \;=\;\frac{n(n+1)}{2}

    \sum^n_{i=1}i^3 \;= \;1^3 + 2^3 + 3^3 + \cdots + n^3 \;=\;\frac{n^2(n+1)^2}{4}

    Yes, the second series is the square of the first.
    . . A fascinating phenomenon, but only a coincidence.
    This "pattern" never shows up again.


    A similar mathmatical joke is: . \begin{Bmatrix}3^2 + 4^2 & = & 5^2 \\<br />
3^3 + 4^3 + 5^3 & = & 6^3 \\<br />
\vdots & & \vdots \end{Bmatrix}

    Once again, these two cases are mere coincidences.
    . . There is no pattern . . .

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  3. #3
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    Squared triangular number - Wikipedia, the free encyclopedia
    Actually ive found this. So it isn't a coincidence.
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