!mathematics identify yourselves
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!r-slurs if you don't want to look like a true r-slur memorizing hundreds of formulas like {n X (n+1) X (2n+1)} to sum the squares from 1 to 14 and then subtract the sum of squares of 1 to 9 the easy thing is to shortcut with number theory.
Each subsequent square increases the difference by 2, each subsequent cube increases the difference by 6
10^2 = 100, 11^2 = 121, difference 21, 21+2 = 23, so 12^ 2 = 121 +23 = 144
So 10^2 + 11^2 +12^2 + 13^2 + 14^2 = 100X5 + 21X4 + 23X3 + 25X2 + 27 = 730
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For the cubes, each subsequent cube increases the difference by (6 * (n-1)) where n is the bigger number being cubed.
so 1³ is 1, 2³ is 8 (difference of [1 + (6 * (2-1))]), 3³ is 27 (difference increased by 12, from 7 to 19), etc.
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Ok moron. Now try taking the 3rd order difference of 1³, 2³, 3³, 4³, 5³
1st order:
|1 - 8| = 7 ; |8-27| = 19 ; |27-64| = 37 ; |64-125| = 61
🍭 𝟤𝓃𝒹 🌸𝓇𝒹𝑒𝓇 🍭
|7 -19| = 12 ; |19 -37| = 18 ; |37 - 61| = 24
‧͙☆༓｡3𝓻𝓭 𝓸𝓻𝓭𝓮𝓻.｡༓☆‧͙
|12-18| = ☆‧͙𝟞‧͙☆ ; |18-24| = ☆‧͙𝟞‧͙☆
Hope that wasn't too hard for you champ. Even the most braindead student learns this in fricking crayon when they're 9.
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no way u really made an alt just to sneed at me about nth order differences when higher order diffs were never mentioned in the first place
surely this is some other devious chad playing an epic prank
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Literally the 4th sentence of his post.
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BIPOC that was the post you made AFTER I had already BUCK checked
your towering skyscraper brain with my 
results-oriented, customer service chad reading comprehension
!r-slurs get your boy he's gone rogue
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There is nothing I can do for the people of this website. You are all human worms.
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That's not me bruh
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You're looking at this the wrong way. If you go by that logic you have to find a new number for every higher order power.
The general rule of power is
(n+1)^k = n^k + X (where x can be calculated via a difference of differences method)
For (n+1)^k the constant difference is found at the k-th difference of differences
And the constant is = (constant for k-1)×k
Constants:
For squares it's 2, found at the just the ordinary difference of differences
For cubes it's 2*3, found at the diff of diff of diff (3rd order)
4th power constant is 6*4 found at the 4th order d-o-d
5th is 24*5 found at the 5th order d-o-d
And so on
!mathematics someone give the generalized algebraic proof to this. It's basic number theory
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https://en.wikipedia.org/wiki/Faulhaber%27s_formula
https://www.emis.de/journals/AMEN/2018/AMEN-170803.pdf
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Neighbor I was just correcting your assertion that the diff increased by 6 between cubes
I'm sure you are correct with all this shit though
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Literally
!mathematics after !math disbanded.
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That fearful neighbor snitching on gauss for finding another counting proof cause I'm jelly
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Not a soul here is white lmao
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I'm transindian you blody blastard bainchod sarrrr
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me when my programming project suddenly requires more than basic high school maths
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The best way to do this is to write (10+n)^2 = 10^2+20n+n^2. That way the whole sum is just 500+20*(1+2+3+4)+1^2+2^2+3^3+4^2. The middle term is 20*10=200, the last sum is easily calculated as 30. Therefore the full sum is 500+200+30=730 and after dividing by 365 we get 2.
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I was out-BIPOCed by collectjism. And I'll tell you here and now, I will never be out-BIPOCed again.
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