# Good dayQuestion: Determine whether the series is convergent or

1. Feb 2, 2012

### dangish

Good day..

Question: Determine whether the series is convergent or divergent:

Series starts at n=1 and goes to infinity.. Of 2/(n*4throot(2n+2))

What I mean is.. 2/(n*(2n+2)^(1/4))

Can someone tell me which test to try? I cant get it in the form of a p-series.. so I think maybe the Integral test would be worth a shot?

2. Feb 2, 2012

### jbunniii

Re: Convergence/Divergence

Can you compare it to a p-series?

3. Feb 2, 2012

### dangish

Re: Convergence/Divergence

Well it sort of looks like it but I can't get it in a form to be confident with an answer

4. Feb 2, 2012

### jbunniii

Re: Convergence/Divergence

Hint:

$$\sum_{n=1}^{\infty} \frac{1}{n*(n)^{1/4}}$$

is a p-series. Does it converge? Can you compare your series to it?

5. Feb 2, 2012

### dangish

Re: Convergence/Divergence

In your example you would get 1/n^(5/4) where p = 5/4 >1 so that would converge.. correct?

I realize mine could be similar... Ʃ[ 2/(n*(2n+2)^(1/4))] But I can't combine the n's on the bottom because the +2 is messing with me.

6. Feb 2, 2012

### jbunniii

Re: Convergence/Divergence

Correct.

How does $1/(2n+2)^{1/4}$ compare with $1/n^{1/4}$? Which one is bigger?

7. Feb 3, 2012

### dangish

Re: Convergence/Divergence

I would like to this 1/(2n+2)^(1/4) is bigger.

8. Feb 3, 2012

### dangish

Re: Convergence/Divergence

Well actually 1/(2n+2)^(1/4) would go to zero faster so I suppose it's smaller?

9. Feb 3, 2012

### jbunniii

Re: Convergence/Divergence

Right. So can you use this fact to apply the comparison test, and conclude that the series converges?