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sloppycanada
 one year ago
I'm so confused on this, I'm not sure what I'm supposed to use for any of this, I don't know the common denominator or anything.
Find the 6th term of the sequence with t1 = 4 and tn = 5tn1.
http://imgur.com/BaADfyq
sloppycanada
 one year ago
I'm so confused on this, I'm not sure what I'm supposed to use for any of this, I don't know the common denominator or anything. Find the 6th term of the sequence with t1 = 4 and tn = 5tn1. http://imgur.com/BaADfyq

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2start with \(4\), and keep multiplying by \(5\) to get the next term.

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1So T6 is 62,500?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2first term, \(\large t_1 ~=~4\) second term, \(\large t_2 ~=~4*5 = 20\) third term, \(\large t_3 ~=~20*5 = 100\) keep going till the 6th term

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1Sorry, I did too many of them. 2500.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2show me the work instead

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1T4 = 100 x 5 = 500 T5 = 500 x 5 = 2500 T6 = 2500 x 5 = 12500

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1And then how do I go about finding the sum of an infinite series?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2look at the terms : \[4,~~20,~~100,~~500,~~2500,~~ \ldots\] what do you notice ? do they seem to converge to some number ?

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1You could go on for ever without getting a sum.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yes, so we say the "sequence doesn't converge" and the infinite sum doesn't exist

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1So for an equation like this  Find the sum of the infinite series 3 + 1.2 + 0.48 + 0.192 + ...if it exists. All I would do is use the formula to find the equation of the infinite series?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2what kind of series is it, geometric/arithmetic ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2there is a nice criterion for testing convergence of geometric series, you simply look at the common ratio

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2whats the common ratio of given series ?

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1The equation is tn/(tn1)

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1Common ratio is 2.5

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2yes work it common ratio = (next term)/(present term)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2looks you have worked it in reverse : (present term)/(next term)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2yes common ratio = 0.4 which is between 1 and 1 so the given series conveges

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2A geometric series converges if the common ratio is between 1 and 1

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2use infinite sum formula to find the sum

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2do you have the formula wid u ?

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1S(infinite) = 3/t.4

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1I have it in my notes

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\[\large S_{\infty} ~=~\dfrac{t_1}{1r}\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\[\large S_{\infty} ~=~\dfrac{3}{10.4}\]

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1I have three more if you have time?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Firs test if the series converges by finding the common ratio

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2whats the common ratio ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yes, which is "not" in between 1 and 1 so the series does not converge.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2we say the sum does not exist

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1Okay so the answer would be "No solution"

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2As you can see, the common ratio decides whether an infinite converges to some number, or if it diverges

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Answer would be "does not converge"

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1If it converges then it has a sum, if it does not converge there is not really a solution?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2yes, do you see why the common ratio of 1.33 gives a diverging sum ?

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1Because it's larger then 1? and not between that 1 and 1

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yes, when you multiply the first term by 1.33, you get a bigger next term; the terms keep growing and the sum wont reach a specific number

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1So for this problem  http://gyazo.com/15138c898cca305ec43a79e298d55821 The answer would be .498

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2how did u get 0.498 ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2im asking because im getting a more nice looking number : 0.5

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2me neither could you show ur work please

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1\[S \infty = \frac{ 1 }{ 3 }\div 1.33\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Ahh okay, you're rounding 1/3 to 0.33

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2i worked it like this : \[\large S_{\infty}~=~\dfrac{1/3}{11/3} = \dfrac{1}{31}=\dfrac{1}{2}=0.5\]

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1I'm not sure why I changed from a fraction to a decimal. Fractions are more precise aren't they?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yep Fractions are exact decimals are not so exact when you get a repeating decimal

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.21/2 = 0.5 both are exact

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.21/3 = 0.33333333333333333333333333... clearly the decimal wont be exact because you can't write out infinitely many 3's

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1Okay, last one  http://gyazo.com/50d340d91d94093d361677d900fa46ee Answer is 1.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\[\huge \color{red}{\checkmark}\]

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1Ah hah! Thank you!

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1Not sure how to show my appreciation on this site (if there are points or something), but let me know if there is.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2yw! click the "Best Response" button next to any reply if you find the answer helpful

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2you could also write a testimonial if you think the helper is amazing

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2not encouraging you to write a testimonial for me right now, but just letting you know :)

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1Finding the sum of an geometric Find S12 for the series 1 + 2 + 4 + 8 +... like this is 49,140

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2go through this when u have time to know more about the site http://openstudy.com/codeofconduct

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2how did u get 49.140 ?

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1Sorry it should be 8,190. 2((12^12)/(12)) = 8190

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435126030016:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2why are you multiplying by 2 ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2first term is 1 right

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2dw:1435126092819:dw

sloppycanada
 one year ago
Best ResponseYou've already chosen the best response.1Okay so it'd just be 4095
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