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MathOnNapkins

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From: Base Tourian

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Posted on 02-24-05 11:08 AM Link
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**
Prier

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Posted on 02-24-05 11:10 AM Link
The answer is 42.
MathOnNapkins

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Posted on 02-24-05 11:26 AM Link
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)
Prier

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Posted on 02-24-05 10:51 PM Link
Could've used 'LOL NO n00b'.

[has no clue]
Smallhacker

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Posted on 02-25-05 12:23 AM Link
Originally posted by MathOnNapkins
I wish I knew more languages to say no in.

Nej (Swedish)
Zem
You can be civil without being flowery, dipshits.
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Posted on 02-25-05 12:26 AM Link
Onay

I'll let you guess where that one's from.
MathOnNapkins

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Posted on 02-25-05 12:52 AM Link
biggus dickus?

spoiler*

-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Spoiler:
n00b = sum(1,you)
neotransotaku

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Posted on 02-25-05 01:15 AM Link
Originally posted by MathOnNapkins
*Predicts that Mutation will come in and say *head explodes**
Heh, 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
MathOnNapkins

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Posted on 02-26-05 08:07 AM Link
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.
Kyoufu Kawa
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Posted on 02-26-05 01:57 PM Link
Originally posted by MathOnNapkins

I wish I knew more languages to say no in.

Nee. (dutch)

And onay is pig latin.
MathOnNapkins

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Posted on 02-28-05 07:57 AM Link
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)
Ran-chan

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Posted on 03-01-05 12:52 AM Link
Originally posted by Kawa-oneechan


And onay is pig latin.


Onay sounds like "Oh no" in swedish. "
Toxic
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Posted on 03-01-05 06:45 AM Link
Ready? lolers


DID U DO THAT ON A NAPKIN??????







I had to
KATW

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Posted on 03-02-05 05:13 AM Link
Jedermann erkl
MathOnNapkins

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Posted on 03-02-05 05:31 AM Link
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.
Zem
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Posted on 03-02-05 08:47 AM Link
Originally posted by MathOnNapkins
I find it funny that I hijacked my own thread :O
CRASH IT INTO TWIN TOWER

I hope no one ever reads that
Kitten Yiffer

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Vivent l'exp����¯�¿�½������©rience de signalisation d'amusement, ou bien !
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Since: 03-15-04
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Posted on 03-02-05 02:11 PM Link
Eh well... Zem...

Which of them?

(edited by Kitten Yiffer on 03-02-05 05:12 AM)
Prier

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Posted on 03-02-05 03:10 PM Link
Originally posted by Zem
...I hope no one ever reads that


GO DIRECTLY TO JAIL! DO NOT PASS GO! DO NOT COLLECT 200 DOLLAH!
Ran-chan

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Posted on 03-02-05 10:09 PM Link
And stay there for 3 turns and pay 100 dollars when you get out.

No one of them, Kitten Yiffer, since they don
neotransotaku

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Posted on 03-03-05 12:07 AM Link
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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