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Syntax Error
Navier-Stokes Equations
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Joined: 28 May 2003
Posts: 1452
Location: Oklahoma
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Mathcounts Challenge: Geometric Series...
Find the sum of the infinite geometric series: 6+3.6+2.16+1.296+...
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- Disco Neal
 Posted: Sun Sep 07, 2003 4:33 pm
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TheSouthpaw
Riemann Hypothesis
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Joined: 25 May 2003
Posts: 257
Location: Boston
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Do what you do with continuing fractions.
The answer, I believe, is 3/2
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Posted: Sun Sep 07, 2003 5:39 pm
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MysticTerminator
Birch & Swinnerton Dyer
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Joined: 27 May 2003
Posts: 3759
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nope. what's with the reference to continuing fractions?
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Posted: Sun Sep 07, 2003 5:40 pm
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Fierytycoon
Navier-Stokes Equations
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Joined: 02 Jun 2003
Posts: 1888
Location: Massachusetts
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What exactly is a "continuing fraction"?
And...
can't you simply find the initial value 6 and the multiplied constant .6 and then sum the geometric series?
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Fierytycoon
Posted: Sun Sep 07, 2003 5:42 pm
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Tare
Navier-Stokes Equations
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Joined: 18 Jul 2003
Posts: 2463
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I think what he means is multiply the common ratio to the whole thing. Then you get the same equation except for the first term*common ratio. Subtract the original equation from that and you get common ratio-1=first term*common ratio, then you could solve the common ratio from there.
For the first time I actually sound like I know the solution! 
Continuing fraction is like 1/3 and 4/7 which the decimal form is continuing, but also repeats itself at some point or another.
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Posted: Sun Sep 07, 2003 5:42 pm
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MysticTerminator
Birch & Swinnerton Dyer
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Joined: 27 May 2003
Posts: 3759
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nope, sorry. A continued fraction is usually a way to write rational numbers. It is of the form 1/(a+1/(b+1/(c+1/(d+1/(e+...)))))
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Posted: Sun Sep 07, 2003 5:46 pm
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TheSouthpaw
Riemann Hypothesis
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Joined: 25 May 2003
Posts: 257
Location: Boston
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Poop on a stick, stupid mistake.
6^1*10^0 + 6^2*10^-1+6^3*10^-2... = x
Factor out 6^1*10^-1
6^1*10^-1 (10 + 6^1*10^ 0...) = x
(3/5) (10 + x) = x
x = 15
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Posted: Sun Sep 07, 2003 5:48 pm
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Tare
Navier-Stokes Equations
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Joined: 18 Jul 2003
Posts: 2463
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Oh, right. Forgot.
Doesn't it repeat itself at some point though?
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Posted: Sun Sep 07, 2003 5:48 pm
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Fierytycoon
Navier-Stokes Equations
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Joined: 02 Jun 2003
Posts: 1888
Location: Massachusetts
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Oh. I knew what continued fractions were, but I didn't know that "continued fractions" were the same as "continuing fractions".
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Fierytycoon
Posted: Sun Sep 07, 2003 5:49 pm
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TheSouthpaw
Riemann Hypothesis
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Joined: 25 May 2003
Posts: 257
Location: Boston
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Wow, all these posts, and I dunno if I'm right or not!
Does anyone else know how to do it another way?
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Posted: Sun Sep 07, 2003 5:51 pm
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MysticTerminator
Birch & Swinnerton Dyer
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Joined: 27 May 2003
Posts: 3759
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Mr. Southpaw, that is correct.
Um....I'm pretty sure they don't repeat for rational numbers...well, they repeat for irrational numbers like :rt2:. They probably don't repeat for irrational numbers like :pi:
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Posted: Sun Sep 07, 2003 5:52 pm
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Tare
Navier-Stokes Equations
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Joined: 18 Jul 2003
Posts: 2463
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I know this is off-topic (so I'll delete this as soon as i get an answer), but is there a reason why everyone refers to TheSouthpaw with Mr.?
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Posted: Sun Sep 07, 2003 6:32 pm
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Syntax Error
Navier-Stokes Equations
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Joined: 28 May 2003
Posts: 1452
Location: Oklahoma
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cause hes brad pitt. duh
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- Disco Neal
Posted: Sun Sep 07, 2003 6:34 pm
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Tare
Navier-Stokes Equations
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Joined: 18 Jul 2003
Posts: 2463
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really
Really? 
...really, Really? 
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Posted: Sun Sep 07, 2003 6:35 pm
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Syntax Error
Navier-Stokes Equations
Offline
Joined: 28 May 2003
Posts: 1452
Location: Oklahoma
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really, mr. southpaw is brad pitt
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- Disco Neal
Posted: Sun Sep 07, 2003 6:37 pm
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Tare
Navier-Stokes Equations
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Joined: 18 Jul 2003
Posts: 2463
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Then shouldn't he be called Mr. Pitt?  Mr. Pitt...that's worse than Mr. Beans :twisted:
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Posted: Sun Sep 07, 2003 6:38 pm
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Syntax Error
Navier-Stokes Equations
Offline
Joined: 28 May 2003
Posts: 1452
Location: Oklahoma
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oh look theres gullible written on the ceiling!
thats all i can say
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- Disco Neal
Posted: Sun Sep 07, 2003 6:44 pm
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Tare
Navier-Stokes Equations
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Joined: 18 Jul 2003
Posts: 2463
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Well if you had just told me the truth all the inintelligent conversation didn't had to happen now, hadn't it. (or should it be "had it"? )
Anyway, when did we start having a ceiling
Besides, I'm too short to write on the ceiling
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Posted: Sun Sep 07, 2003 6:52 pm
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Rep123max
Navier-Stokes Equations
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Joined: 30 Jun 2003
Posts: 1992
Location: Texas
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i
i havent read the other messages im just posting my solution:
Spoiler:
the sum of a geometric series with a as the first term and r as what you multiply each term by=a/(1-r) so its 6/(1-.6)=6/.4=15
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Posted: Sun Sep 07, 2003 6:52 pm
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Tare
Navier-Stokes Equations
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Joined: 18 Jul 2003
Posts: 2463
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Da, that is korrekt. (and it's misspelled for a reason )
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Posted: Sun Sep 07, 2003 6:55 pm
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