Daily Maths Challenges

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siriusmart

[2024/05/09] Sum of n squares (lemmy.world)

submitted 7 months ago by siriusmart to c/dailymaths

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Show that the sum of the first n squares is n(n+1)(2n+1)/6.
I know this is often in the textbook for proof by induction, which is why proof by induction is not allowed.

This is a relatively hard one, take your time.

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[–] siriusmart 3 points 7 months ago (1 children)

i took the second setup cuz thats what i saw when thinking of the problem, i'll read the first approach later

[–] zkfcfbzr 3 points 7 months ago* (last edited 7 months ago)

I did see a third setup where you take Σ (i = 1 to n) (Σ (k = 1 to i) 2k-1), which is a valid setup where you count all the blocks on the top of their column, then remove those and count the new top blocks, etc - but it ended up not leading to a proof of the formula because as it turns out, there are always i^2 (from i = n to 1) blocks on the top layer. So it's just a worse way of doing Σi^2 and we get a 0 = 0 situation.