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

  • Thread starter kuczmama
  • Start date
  • #1
11
0

Homework Statement


infinity
Ʃ(2n+3n)/(4n+1)
n=0

Homework Equations


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



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.
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,556
767
Think about geometric series.
 
  • #3
11
0
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
 
  • #4
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,556
767
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
Break it up into two problems and factor a 4 out of the denominator.
 
  • #5
11
0
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?
 
  • #6
11
0
I cant find a common r value. I don't think it is a geometric series. So I am pretty lost still.
 
  • #7
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,556
767
Break it up into two problems and factor a 4 out of the denominator.
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?
I cant find a common r value. I don't think it is a geometric series. So I am pretty lost still.
Yes you can break it up like that. It makes two separate problems. What about my other suggestion in red above?
 
  • #8
11
0
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
 
  • #9
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,556
767
[tex]\frac 1 {4^{n+1}} = \frac 1 4\cdot\frac 1 {4^n}[/tex]
 
  • #10
11
0
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.
 

Related Threads on Determine whether the following series converes or diverges and find the sum

Replies
8
Views
3K
Replies
15
Views
6K
Replies
1
Views
1K
Replies
3
Views
4K
Replies
2
Views
2K
Replies
3
Views
373
Replies
1
Views
3K
Replies
2
Views
2K
Replies
2
Views
620
Replies
11
Views
9K
Top