Mathcounts Challenge: Geometric Series...

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Find the sum of the infinite geometric series: 6+3.6+2.16+1.296+...

[TheSouthpaw]

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Do what you do with continuing fractions.

The answer, I believe, is 3/2

[MysticTerminator]

nope. what's with the reference to continuing fractions?

[Fierytycoon]

What exactly is a "continuing fraction"?

And... Click to reveal hidden content

can't you simply find the initial value 6 and the multiplied constant .6 and then sum the geometric series?

[Tare]

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.

[MysticTerminator]

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+...)))))

[TheSouthpaw]

Poop on a stick, stupid mistake.

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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

[Tare]

Oh, right. Forgot.
Doesn't it repeat itself at some point though?

[Fierytycoon]

Oh. I knew what continued fractions were, but I didn't know that "continued fractions" were the same as "continuing fractions".

[TheSouthpaw]

Wow, all these posts, and I dunno if I'm right or not!

Does anyone else know how to do it another way?

[MysticTerminator]

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:

[Tare]

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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cause hes brad pitt. duh

[Tare]

really

Really?

...really, Really?

[Syntax Error]

really, mr. southpaw is brad pitt

[Tare]

Then shouldn't he be called Mr. Pitt? Mr. Pitt...that's worse than Mr. Beans :twisted:

[Syntax Error]

oh look theres gullible written on the ceiling!


thats all i can say

[Tare]

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

[Rep123max]

i havent read the other messages im just posting my solution:
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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

[Tare]

Da, that is korrekt. (and it's misspelled for a reason )