Not sure what kind of maths but I think its summination

**Dark Ainur** · September 21st 2007, 12:28 PM

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?

**Soroban** · September 24th 2007, 07:39 AM

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 . . .

**Dark Ainur** · September 24th 2007, 08:34 AM

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

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