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sequence problem _ Calculus

Mathematics
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|dw:1351476871325:dw|
don't I need to use some formula?
So is the question, "Does the series converge?" ? :o

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Other answers:

yes, I know it converges to 9/4
doesn't help that I don't know why?
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|dw:1351477186152:dw| Hmm can't you do some type of comparison test? Sorry I'm a little rusty with these :D We know that the p-series 1/n^2 converses, and our series is smaller than that one :O something like that..
|dw:1351477424396:dw|
I am as rusty as you
Hmm :[
how about if I do this as a telescoping series? as if I know what I am talking about
Yah that's prolly the way to approach it c: try to recognize a pattern coming out of it.
I know if I factor out the 9 and then I just need to create the (1/4)
Oh oh oh i think it's coming back to me a little bit... I think in order to write it as a telescoping series, we need to rewrite it as partial fractions, then we'll get terms being subtracted in each n, allowing for some cancellations probably.
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oh sorry XD hehe
sorry, I ran off to watch some youtube videos on this
Mmmm that's prolly a good idea :) I don't think I'm getting anywhere with this one lol
|dw:1351479960238:dw|got this as well
|dw:1351480090695:dw|
the next few terms are something like (1/8-1/5+1/12)+(1/10-1/6+1/14)
I thought somehow we would be left with 1/4 as the first term then it would make sense that they solution is 9/4
wonder if we messed up on the partial fraction
I don't think so
Ummm I doubt it, it's likely that the terms just cancel out in a strange way :D
well that is good to know
yes, wonder if we have to do more than the first three terms to see it
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Oh hmm :D
ok that is all I see right now
nasty little problem :3
yes, well I think I will sleep on it, would not be the first time I went to bed with an unsolved problem....thanks..........
|dw:1351531637965:dw|ok I think I solved it @zepdrix
Hmmmmmm that doesn't quite look right <:o you can't split up the base of a fraction. \[\frac{ 1 }{ 2n+4 }=\frac{ 1 }{ \infty+4 }=0\]
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