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

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.

LCKurtz
Homework Helper
Gold Member

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

LCKurtz
Homework Helper
Gold Member
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.

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.

LCKurtz
Homework Helper
Gold Member
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?

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

LCKurtz
$$\frac 1 {4^{n+1}} = \frac 1 4\cdot\frac 1 {4^n}$$