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Mathcounts Challenge: Geometric Series...
Moderators: frost13, kyyuanmathcount, LadyKn1ght, nebula42, rcv, solafidefarms
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Syntax Error
Navier-Stokes Equations
Navier-Stokes Equations

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Joined: 28 May 2003
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Location: Oklahoma
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#1
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

PostPosted: Sun Sep 07, 2003 4:33 pm  Back to top 
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TheSouthpaw
Riemann Hypothesis
Riemann Hypothesis


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#2


Do what you do with continuing fractions.

The answer, I believe, is 3/2



PostPosted: Sun Sep 07, 2003 5:39 pm  Back to top 
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MysticTerminator
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#3
nope. what's with the reference to continuing fractions?

PostPosted: Sun Sep 07, 2003 5:40 pm  Back to top 
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Fierytycoon
Navier-Stokes Equations
Navier-Stokes Equations

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#4
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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PostPosted: Sun Sep 07, 2003 5:42 pm  Back to top 
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Navier-Stokes Equations
Navier-Stokes Equations

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#5
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! Smile

Continuing fraction is like 1/3 and 4/7 which the decimal form is continuing, but also repeats itself at some point or another.

PostPosted: Sun Sep 07, 2003 5:42 pm  Back to top 
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MysticTerminator
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#6
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+...)))))

PostPosted: Sun Sep 07, 2003 5:46 pm  Back to top 
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TheSouthpaw
Riemann Hypothesis
Riemann Hypothesis


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#7
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



PostPosted: Sun Sep 07, 2003 5:48 pm  Back to top 
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Navier-Stokes Equations
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#8
Oh, right. Forgot.
Doesn't it repeat itself at some point though?

PostPosted: Sun Sep 07, 2003 5:48 pm  Back to top 
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Fierytycoon
Navier-Stokes Equations
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#9
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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PostPosted: Sun Sep 07, 2003 5:49 pm  Back to top 
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TheSouthpaw
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#10
Wow, all these posts, and I dunno if I'm right or not!

Does anyone else know how to do it another way?

PostPosted: Sun Sep 07, 2003 5:51 pm  Back to top 
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MysticTerminator
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#11
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:

PostPosted: Sun Sep 07, 2003 5:52 pm  Back to top 
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#12
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.?

PostPosted: Sun Sep 07, 2003 6:32 pm  Back to top 
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Syntax Error
Navier-Stokes Equations
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#13
cause hes brad pitt. duh
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PostPosted: Sun Sep 07, 2003 6:34 pm  Back to top 
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#14
really Smile

Really? Mr. Green

...really, Really? Razz

PostPosted: Sun Sep 07, 2003 6:35 pm  Back to top 
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Syntax Error
Navier-Stokes Equations
Navier-Stokes Equations

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#15
really, mr. southpaw is brad pitt
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PostPosted: Sun Sep 07, 2003 6:37 pm  Back to top 
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#16
Then shouldn't he be called Mr. Pitt? Very Happy Mr. Pitt...that's worse than Mr. Beans :twisted:

PostPosted: Sun Sep 07, 2003 6:38 pm  Back to top 
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Syntax Error
Navier-Stokes Equations
Navier-Stokes Equations

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#17
oh look theres gullible written on the ceiling!


thats all i can say
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PostPosted: Sun Sep 07, 2003 6:44 pm  Back to top 
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#18
Well if you had just told me the truth all the inintelligent Smile conversation didn't had to happen now, hadn't it. (or should it be "had it"? Smile )

Anyway, when did we start having a ceiling Mr. Green
Besides, I'm too short to write on the ceiling Razz

PostPosted: Sun Sep 07, 2003 6:52 pm  Back to top 
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Rep123max
Navier-Stokes Equations
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#19
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

PostPosted: Sun Sep 07, 2003 6:52 pm  Back to top 
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#20
Da, that is korrekt. (and it's misspelled for a reason Smile )

PostPosted: Sun Sep 07, 2003 6:55 pm  Back to top 
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