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Acmlm's Board - I2 Archive - Lost Section - Sums of powers | | | Thread closed |
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MathOnNapkins Math n' Hacks Level: 67 Posts: 1479/2189 EXP: 2495887 For next: 96985 Since: 03-18-04 From: Base Tourian Since last post: 1 hour Last activity: 32 min. |
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Don't know how many math geeks there are on the board. Certainly a good number of number geeks. Question: If you go to websites and look for partial sums of integers, squares, cubes, etc. you will find induction proofs verifying that the formulas they give are true. But I have yet to see a website that gives the derivation of these formulas. In fact, for even powers this is not exactly trivial. I invite anyone to try a proof of this: sum of the first n squares of integers = 12 + 22 + ... + n2 = n(n-1)(2n-1)/6 derive the formula directly. the proof of 1 + 2 + ... + n = n(n+1)/2 is fairly straightforward. take n + (n-1) + (n-2) + ... + (n-(n-1)) + (n-(n-0)) as a reformulation of the sequence. That breaks down to (n+1) terms of n, i.e. n(n+1), minus the nth sum of integers = the nth sum of integers. notationally: sum(1,n) = n(n+1) - sum(1,n) Then 2sum(1,n) = n(n+1) which reduces to sum(1,n) = n(n+1)/2 Don't try a derivation of this kind for squares, you'll get no where. You need to be sneakier. Then, if you want, apply this to sum(14,n4), the same kind of proof applies, just more complicated. The sum of odd powers can be found from the sums of all lower powers, so it depends upon even powers. *Predicts that Mutation will come in and say *head explodes** |
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Prier Archangel Administrative Priestess. NUCLEAR SUB WEEEOOOO Level: 119 Posts: 5471/8392 EXP: 18790939 For next: 138352 Since: 03-15-04 From: Nerima Dist. - Tokyo, Japan Since last post: 1 day Last activity: 1 day |
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The answer is 42. | |||
MathOnNapkins Math n' Hacks Level: 67 Posts: 1482/2189 EXP: 2495887 For next: 96985 Since: 03-18-04 From: Base Tourian Since last post: 1 hour Last activity: 32 min. |
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No. いいえ لا ουκ Non. Non. (latin) No. (spanish) nein I wish I knew more languages to say no in. How about if(1 == 0) { yes(); } else { no(); } I need to hire David Spade (edited by MathOnNapkins on 02-24-05 02:27 AM) |
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Prier Archangel Administrative Priestess. NUCLEAR SUB WEEEOOOO Level: 119 Posts: 5472/8392 EXP: 18790939 For next: 138352 Since: 03-15-04 From: Nerima Dist. - Tokyo, Japan Since last post: 1 day Last activity: 1 day |
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Could've used 'LOL NO n00b'. [has no clue] |
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Smallhacker Green Birdo SMW Hacking Moderator Level: 68 Posts: 1332/2273 EXP: 2647223 For next: 81577 Since: 03-15-04 From: Söderhamn, Sweden Since last post: 10 hours Last activity: 9 hours |
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Originally posted by MathOnNapkins Nej (Swedish) |
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Zem You can be civil without being flowery, dipshits. Level: 49 Posts: 845/1107 EXP: 829398 For next: 54485 Since: 06-13-04 Since last post: 131 days Last activity: 131 days |
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Onay I'll let you guess where that one's from. |
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MathOnNapkins Math n' Hacks Level: 67 Posts: 1491/2189 EXP: 2495887 For next: 96985 Since: 03-18-04 From: Base Tourian Since last post: 1 hour Last activity: 32 min. |
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biggus dickus? spoiler* - - - - - - - - - - - - - - - Spoiler: n00b = sum(1,you) |
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neotransotaku Baby Mario 戻れたら、 誰も気が付く Level: 87 Posts: 2413/4016 EXP: 6220548 For next: 172226 Since: 03-15-04 From: Outside of Time/Space Since last post: 11 hours Last activity: 1 hour |
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Originally posted by MathOnNapkinsHeh, I'll be the first *head explodes* Anyways, the proof has to do with induction--so I guess the question is how did they derive the end point in the first place |
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MathOnNapkins Math n' Hacks Level: 67 Posts: 1499/2189 EXP: 2495887 For next: 96985 Since: 03-18-04 From: Base Tourian Since last post: 1 hour Last activity: 32 min. |
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Okay, hint time. The sum of the first m odd integers is equal to m2 this is where I got stuck for a looong time. |
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Kyoufu Kawa I'm not bad. I'm just drawn that way. Level: 70 Posts: 1229/2481 EXP: 3008456 For next: 7355 Since: 03-19-04 From: Catgirl Central Since last post: 14 hours Last activity: 13 hours |
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Originally posted by MathOnNapkins Nee. (dutch) And onay is pig latin. |
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MathOnNapkins Math n' Hacks Level: 67 Posts: 1517/2189 EXP: 2495887 For next: 96985 Since: 03-18-04 From: Base Tourian Since last post: 1 hour Last activity: 32 min. |
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Actually, I lied, the answer is 42. edit: funny thing is: if I had asked this on #metroid on irc.metroid2002.com, like 30 people would have known how to do this. (edited by MathOnNapkins on 02-27-05 10:58 PM) |
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Ran-chan Moldorm eek, when are they going to stop growing... Level: 143 Posts: 7852/12781 EXP: 35293588 For next: 538220 Since: 03-15-04 From: Nerima District, Tokyo - Japan Since last post: 12 hours Last activity: 12 hours |
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Originally posted by Kawa-oneechan Onay sounds like "Oh no" in swedish. " |
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Toxic in a sublime state of mind Level: 75 Posts: 2496/2857 EXP: 3732709 For next: 94195 Since: 03-15-04 Since last post: 3 days Last activity: 8 hours |
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Ready? lolers DID U DO THAT ON A NAPKIN?????? I had to |
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KATW King Yoshi "If you stare at something long enough, it can be funny." Level: 86 Posts: 2636/3959 EXP: 6087979 For next: 54128 Since: 03-15-04 Since last post: 7 hours Last activity: 5 hours |
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Jedermann erkl | |||
MathOnNapkins Math n' Hacks Level: 67 Posts: 1530/2189 EXP: 2495887 For next: 96985 Since: 03-18-04 From: Base Tourian Since last post: 1 hour Last activity: 32 min. |
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I find it funny that I hijacked my own thread :O anyways sum(1,n2) = 1 + 22 + ... + n2 = 1 1 + 3 1 + 3 + 5 ... 1 + 3 + 5 ... + (2n-1) = sum(from k=1 to k=n, (n+1-k)(2k-1)) which you can evaluate out in terms of the sums of integers, rather than squares. Napkins lol. Nope, but I used to, hence the name. |
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Zem You can be civil without being flowery, dipshits. Level: 49 Posts: 866/1107 EXP: 829398 For next: 54485 Since: 06-13-04 Since last post: 131 days Last activity: 131 days |
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Originally posted by MathOnNapkinsCRASH IT INTO TWIN TOWER I hope no one ever reads that |
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Kitten Yiffer Purple wand Furry moderator Vivent l'exp����¯�¿�½������©rience de signalisation d'amusement, ou bien ! Level: 135 Posts: 8204/11162 EXP: 28824106 For next: 510899 Since: 03-15-04 From: Sweden Since last post: 3 hours Last activity: 4 min. |
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Eh well... Zem... Which of them? (edited by Kitten Yiffer on 03-02-05 05:12 AM) |
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Prier Archangel Administrative Priestess. NUCLEAR SUB WEEEOOOO Level: 119 Posts: 5524/8392 EXP: 18790939 For next: 138352 Since: 03-15-04 From: Nerima Dist. - Tokyo, Japan Since last post: 1 day Last activity: 1 day |
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Originally posted by Zem GO DIRECTLY TO JAIL! DO NOT PASS GO! DO NOT COLLECT 200 DOLLAH! |
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Ran-chan Moldorm eek, when are they going to stop growing... Level: 143 Posts: 7883/12781 EXP: 35293588 For next: 538220 Since: 03-15-04 From: Nerima District, Tokyo - Japan Since last post: 12 hours Last activity: 12 hours |
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And stay there for 3 turns and pay 100 dollars when you get out. No one of them, Kitten Yiffer, since they don |
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neotransotaku Baby Mario 戻れたら、 誰も気が付く Level: 87 Posts: 2510/4016 EXP: 6220548 For next: 172226 Since: 03-15-04 From: Outside of Time/Space Since last post: 11 hours Last activity: 1 hour |
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Crash it in to gamefaqs? Gamefaqs is a company with a building and a paid CEO and paid staff and what not? Where are they located? |
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