precal
  • precal
sequence problem _ Calculus
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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precal
  • precal
|dw:1351476871325:dw|
precal
  • precal
don't I need to use some formula?
zepdrix
  • zepdrix
So is the question, "Does the series converge?" ? :o

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precal
  • precal
yes, I know it converges to 9/4
precal
  • precal
doesn't help that I don't know why?
precal
  • precal
|dw:1351477345222:dw|
precal
  • precal
|dw:1351477381056:dw|
zepdrix
  • zepdrix
|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..
precal
  • precal
|dw:1351477424396:dw|
precal
  • precal
I am as rusty as you
zepdrix
  • zepdrix
Hmm :[
precal
  • precal
how about if I do this as a telescoping series? as if I know what I am talking about
zepdrix
  • zepdrix
Yah that's prolly the way to approach it c: try to recognize a pattern coming out of it.
precal
  • precal
I know if I factor out the 9 and then I just need to create the (1/4)
zepdrix
  • zepdrix
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.
anonymous
  • anonymous
*
zepdrix
  • zepdrix
|dw:1351478870156:dw|
zepdrix
  • zepdrix
|dw:1351479010862:dw|
anonymous
  • anonymous
|dw:1351479486392:dw|
zepdrix
  • zepdrix
oh sorry XD hehe
precal
  • precal
sorry, I ran off to watch some youtube videos on this
zepdrix
  • zepdrix
Mmmm that's prolly a good idea :) I don't think I'm getting anywhere with this one lol
precal
  • precal
|dw:1351479960238:dw|got this as well
precal
  • precal
|dw:1351480090695:dw|
anonymous
  • anonymous
the next few terms are something like (1/8-1/5+1/12)+(1/10-1/6+1/14)
precal
  • precal
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
precal
  • precal
wonder if we messed up on the partial fraction
anonymous
  • anonymous
I don't think so
zepdrix
  • zepdrix
Ummm I doubt it, it's likely that the terms just cancel out in a strange way :D
precal
  • precal
well that is good to know
precal
  • precal
yes, wonder if we have to do more than the first three terms to see it
zepdrix
  • zepdrix
|dw:1351480321431:dw|
precal
  • precal
|dw:1351480632232:dw|
zepdrix
  • zepdrix
Oh hmm :D
precal
  • precal
ok that is all I see right now
zepdrix
  • zepdrix
nasty little problem :3
precal
  • precal
yes, well I think I will sleep on it, would not be the first time I went to bed with an unsolved problem....thanks..........
precal
  • precal
|dw:1351531637965:dw|ok I think I solved it @zepdrix
zepdrix
  • zepdrix
Hmmmmmm that doesn't quite look right <:o you can't split up the base of a fraction. \[\frac{ 1 }{ 2n+4 }=\frac{ 1 }{ \infty+4 }=0\]
zepdrix
  • zepdrix
|dw:1351531992905:dw|