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Mathematics 12 Online
OpenStudy (lovelyharmonics):

geometric sequencing

OpenStudy (anonymous):

what about it?

OpenStudy (lovelyharmonics):

Find the sum of the geometric sequence. \[1, \frac{ 1 }{ 2 }, \frac{ 1 }{ 4 }, \frac{ 1 }{ 8 }, \frac{ 1 }{ 16 } \]

OpenStudy (lovelyharmonics):

i get that the pattern is multiplying it by 1/2 but i dont understand how to find the sum

OpenStudy (luigi0210):

I think there's a formula for adding geometric sequences, isn't there?

OpenStudy (lovelyharmonics):

yeah this website lists it http://www.mathsisfun.com/algebra/sequences-sums-geometric.html but it dosent tell me how to get to the sum :c

OpenStudy (luigi0210):

Just use this formula: http://prntscr.com/3eov4p

OpenStudy (lovelyharmonics):

i think @halorazer thinks your a girl cuz he just messaged me that you want the d...... but he seems to think your a girl

OpenStudy (lovelyharmonics):

okay so this is the equation but how do i know whats what? .-. @Luigi0210

OpenStudy (anonymous):

It's true, Luigi wants the D.

OpenStudy (anonymous):

Anyways, for your question. Can you identify whether or not the sequence is finite or infinite?

OpenStudy (lovelyharmonics):

lol i don't need your help @halorazer your just a nuisance, thus i bid you farewell

OpenStudy (anonymous):

Oh, okay. Let's call names shall we.

OpenStudy (lovelyharmonics):

-.- this is exactly why i dont want you on my question...... now @Luigi0210 how do you tell the different parts apart? .-.

OpenStudy (luigi0210):

Bro, please ;) And let him help. I have something to do in the meanwhile ._.

OpenStudy (anonymous):

Brofist, Luigi. :3

OpenStudy (anonymous):

So do tell me, what is the common ratio between values?

OpenStudy (lovelyharmonics):

i hate you ಠ╭╮ಠ

OpenStudy (anonymous):

Eh, you're not the first. I'm helping you though, so.

OpenStudy (lovelyharmonics):

yay your back! ✧・゚:*✧・゚:* \(◕‿◕✿)/ *:・゚✧*:・゚✧

OpenStudy (anonymous):

I was talking to the female companion, am sorri.

OpenStudy (anonymous):

Can you pls read dis http://www.urbandictionary.com/define.php?term=suck%20my%20ass I do believe what I said was "suck my retrice" Asses go in, therefore you cannot suck it.

OpenStudy (ranga):

Sum of the first "n" terms of a geometric series: \[a\frac{1-r^n}{1-r}\]Sum of an infinite geometric series: \[\frac{a}{1-r}\]where a is the first term r is the common ratio. n is the number of terms.

OpenStudy (lovelyharmonics):

thank you @ranga @halorazer ~mabey you could learn a thing or two from helpful people such as this -.-

OpenStudy (ranga):

You are welcome.

OpenStudy (lovelyharmonics):

okay so it would be \[1\frac{ 1-\frac{ 1 }{ 2 }^{5} }{ 1-\frac{ 1 }{ 2 } }\]

OpenStudy (anonymous):

It's a bit difficult to help someone that won't let someone help them. And that's why I get medals on 86% of my answers. :)

OpenStudy (lovelyharmonics):

no you only get medals from the people you arnt complete bicth to

OpenStudy (anonymous):

Which is erryone. It's funny, because I treat everyone the same and no one else complains. Is something wrong?

OpenStudy (lovelyharmonics):

yeah, with you mabey

OpenStudy (ranga):

Yes, that would be the sum of the 5 terms of the given geometric sequence. Just need to simplify it. FYI: People have the option to block others by positioning the mouse over the person's name, and clicking on 'Block User'.

OpenStudy (anonymous):

It's a fancy button isn't it. She'd much rather insult me than block me.

OpenStudy (lovelyharmonics):

youd much rather have sex with me than block me .-. youve said so on several occasions

OpenStudy (anonymous):

I have never blocked someone on here. I believe in peaceful resolutions. You, however, are more than welcome to block me. :3 I'm sorry you feel the need to do so.

OpenStudy (lovelyharmonics):

okay so simplifying it, the 1s would cancel out and leave you with \[1\frac{ \frac{ 1 }{ 2 }^5 }{ \frac{ 1 }{ 2 } }\] but 1/2 ^5 is 1/32.... so then its

OpenStudy (ranga):

It is \[\Large 1\frac{ 1 - \frac{ 1 }{ 2 }^5 }{ \frac{ 1 }{ 2 } }\]

OpenStudy (lovelyharmonics):

.-. \[1 \frac{ 1-\frac{ 1 }{ 32 } }{ \frac{ 1 }{ 2 } }\]

OpenStudy (ranga):

simplify further. 1 - 1/32 = ? dividing by 1/2 is same as multiplying by 2.

OpenStudy (lovelyharmonics):

it would be -31/32?

OpenStudy (ranga):

1 - 1/32 = +31/32 divide 31/32 by 1/2 or multiply 31/32 * 2/1 = 31/16

OpenStudy (lovelyharmonics):

which would equal 2 and 15/16 c:

OpenStudy (ranga):

You can verify the sum is correct by simply adding the 5 terms: 1 + 1/2 + 1/4 + 1/8 + 1/16 = 16/16 + 8/16 + 4/16 + 2/16 + 1/16 = (16+8+4+2+1)/16 = 31/16

OpenStudy (lovelyharmonics):

.-. but 2 15/16 isnt one of my answers, infact its nowhere near any of my answers

OpenStudy (ranga):

16 goes into 31 just once (not 2).

OpenStudy (lovelyharmonics):

yeah but in front of the whole problem there was a 1

OpenStudy (ranga):

That 1 after you plug into the formula is a multiplication and not an addition.

OpenStudy (ranga):

It is \[a * \frac{1-r^n}{1-r} = 1 * \frac{1-1/2^n}{1-1/2} \]

OpenStudy (ranga):

You don't see 1 & 15/16 or 31 / 16 among the answer choices?

OpenStudy (lovelyharmonics):

no.... Find the sum of the geometric sequence. 1, one divided by two, one divided by four, one divided by eight, one divided by sixteen one divided by twelve 93 negative one divided by forty eight thirty one divided by sixteen

OpenStudy (ranga):

last choice.

OpenStudy (lovelyharmonics):

oh okay c: thank you

OpenStudy (ranga):

yw.

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