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

• Sep 21st 2007, 12:28 PM
Dark Ainur
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.

http://www.math.ucdavis.edu/%7Ekouba...ctory/img5.gif
http://www.math.ucdavis.edu/%7Ekouba...ctory/img7.gif
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?
• Sep 24th 2007, 07:39 AM
Soroban
Hello, Dark Ainur!

Quote:

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

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

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: .$\displaystyle \begin{Bmatrix}3^2 + 4^2 & = & 5^2 \\ 3^3 + 4^3 + 5^3 & = & 6^3 \\ \vdots & & \vdots \end{Bmatrix}$

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

• Sep 24th 2007, 08:34 AM
Dark Ainur
Squared triangular number - Wikipedia, the free encyclopedia
Actually ive found this. So it isn't a coincidence.