/h/nerdshit House Racist
nuclearshill gau/cho  2mo ago (image post) 330 thread views #296301

Dramatards doing the maths :marseymath:

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!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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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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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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https://en.wikipedia.org/wiki/Faulhaber%27s_formula

https://www.emis.de/journals/AMEN/2018/AMEN-170803.pdf

:#sigmacap: :#questionmark:

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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 :marseykekw:

surely this is some other devious chad playing an epic prank :marseyoctopus2:

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For (n+1)^k the constant difference is found at the k-th difference of differences

Literally the 4th sentence of his post.

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BIPOC that was the post you made AFTER I had already BUCK checked :marseytariq: your towering skyscraper brain with my :marseynerd3: 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 :#marseyfacepalm:

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