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Determine whether the following series converes or diverges and find the sum

  1. Oct 30, 2011 #1
    1. The problem statement, all variables and given/known data
    infinity
    Ʃ(2n+3n)/(4n+1)
    n=0

    2. Relevant equations
    We learned the integral test. The p-series. The nth term test.



    3. The attempt at a solution
    I figured out that the terms are positive and that they approach 0. the first couple of terms are (2/4)+ 5/16+13/64+35/256+...

    I think I can use the integral test, but that only tells me whether or not it converges. I think that it does. However, I don't know how to find its sum. If you guys could help me out I would really appreciate it.
     
  2. jcsd
  3. Oct 30, 2011 #2

    LCKurtz

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    Think about geometric series.
     
  4. Oct 30, 2011 #3
    I know that a geometric series is like a+ar+ar2+ar3+...arn, but I dont know how to re-write this in that form
     
  5. Oct 30, 2011 #4

    LCKurtz

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    Break it up into two problems and factor a 4 out of the denominator.
     
  6. Oct 30, 2011 #5
    do you mean break it up into two integrals? or would it be like

    Ʃ2n/4n+1 +Ʃ 3n/4n+1

    Can you break it up like that?
     
  7. Oct 30, 2011 #6
    I cant find a common r value. I don't think it is a geometric series. So I am pretty lost still.
     
  8. Oct 30, 2011 #7

    LCKurtz

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    Yes you can break it up like that. It makes two separate problems. What about my other suggestion in red above?
     
  9. Oct 30, 2011 #8
    this is probably a dumb question, but how do I factor something out if it is a sequence. I really don't know how to factor a 4 out of the denominator. like would I multiply the problem by 1/4
     
  10. Oct 30, 2011 #9

    LCKurtz

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    [tex]\frac 1 {4^{n+1}} = \frac 1 4\cdot\frac 1 {4^n}[/tex]
     
  11. Oct 30, 2011 #10
    Ohh ok. Thank you so much. I just figured it out. I now know that the sum is (3/2). I didnt know you could factor it out like that. that helps so much.
     
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