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http://mathoverflow.net/questions/8846/proofs-without-words/69756#69756

BTW: Nice site.

No ._.

wait

Is it like this?
(2n+1)+2(2n+1)+3(2n+1)+...+n(2n+1)

exactly - now factor out the (2n+1)

\[\frac{n\left(n+1\right) \left(2n+1\right)}2\]What about the six?

that is correct - now you have to subtract the sum of the previous 2 triangles from this

but why?

what you are trying to find is the sum of the numbers in the 1st triangle

\[1^1+2^2+3^3+...\]

that should have started with \(1^2\)

it is a visual proof of this sum

oh I see it

thanks, i will try my best.

let me know if you require a clue.

when you do "see" how to do it - it is quite remarkable!

this really is a "visual" solution - so don't think about any complex math here

OMG this is the best proof I have seen in my life so far

:) glad you "saw" it at last!

it is a very pleasing proof

it is. and thanks a lot asnaseer. :-)

yw :)

really beautiful xD