## precal 2 years ago sequence problem _ Calculus

1. precal

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2. precal

don't I need to use some formula?

3. zepdrix

So is the question, "Does the series converge?" ? :o

4. precal

yes, I know it converges to 9/4

5. precal

doesn't help that I don't know why?

6. precal

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7. precal

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8. 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..

9. precal

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10. precal

I am as rusty as you

11. zepdrix

Hmm :[

12. precal

how about if I do this as a telescoping series? as if I know what I am talking about

13. zepdrix

Yah that's prolly the way to approach it c: try to recognize a pattern coming out of it.

14. precal

I know if I factor out the 9 and then I just need to create the (1/4)

15. 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.

16. colorful

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17. zepdrix

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18. zepdrix

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19. colorful

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20. zepdrix

oh sorry XD hehe

21. precal

sorry, I ran off to watch some youtube videos on this

22. zepdrix

Mmmm that's prolly a good idea :) I don't think I'm getting anywhere with this one lol

23. precal

|dw:1351479960238:dw|got this as well

24. precal

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25. colorful

the next few terms are something like (1/8-1/5+1/12)+(1/10-1/6+1/14)

26. 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

27. precal

wonder if we messed up on the partial fraction

28. colorful

I don't think so

29. zepdrix

Ummm I doubt it, it's likely that the terms just cancel out in a strange way :D

30. precal

well that is good to know

31. precal

yes, wonder if we have to do more than the first three terms to see it

32. zepdrix

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33. precal

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34. zepdrix

Oh hmm :D

35. precal

ok that is all I see right now

36. zepdrix

nasty little problem :3

37. 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..........

38. precal

|dw:1351531637965:dw|ok I think I solved it @zepdrix

39. zepdrix

Hmmmmmm that doesn't quite look right <:o you can't split up the base of a fraction. $\frac{ 1 }{ 2n+4 }=\frac{ 1 }{ \infty+4 }=0$

40. zepdrix

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