@ColinTheMathmo: is this: http://www.bowdoin.edu/~ltoma/teaching/cs340/spring05/coursestuff/Bentley_BumperSticker.pdf something you’ve seen before?
Proof
Let \(S = \sum_{r=1}^n r^2\).
Then \(S = \\
1+\\
2+2+\\
3+3+3+\\
\cdots \\
n+n+n+\cdots+n\)
Also, \(S = \\
n+\\
n+(n-1)+\\
n+(n-1)+(n-2)+\\
\cdots \\
n+(n-1)+(n-2)+\cdots+2+1\)
And \(S = \\
n+\\
(n-1)+n+\\
(n-2)+(n-1)+n+\\
\cdots \\
1+2+3+\cdots+(n-1)+n\)
So \(S+S+S = \\
(2n+1)+\\
(2n+1)+(2n+1)+\\
(2n+1)+(2n+1)+(2n+1)+\\
\cdots \\
(2n+1)+(2n+1)+(2n+1)+\cdots+(2n+1)+(2n+1)\)
i.e., \(3S = (2n+1) \times \frac{n(n+1)}{2}\) or \(S = \frac{1}{6} n(n+1)(2n+1)\) #proofinatoot (via Jeremy Kun)
But for ellipses
We'd have no eclipses
#groot
#reckonthatmustbetrue
A post that features some of my Mathstodon tooters: http://www.flyingcoloursmaths.co.uk/summary-summery-summation/
A young man defeats several martial arts masters by inventing a martial art that depends solely on his infallibly good luck. He names it Bullshitsu.
#writingprompts #writing
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@ColinTheMathmo I would consider a delay in email a feature, not a bug. People seem to confuse email with instant messaging. Email is supposed to be asynchronous. I guess some instant messaging tools are also supposed to be asynch, but apparently everything should be like SMS. #getofmylawn
A mathematician with nothing to prove.