Good dayQuestion: Determine whether the series is convergent or

[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 can't get it in the form of a p-series.. so I think maybe the Integral test would be worth a shot?

 

[jbunniii]

Can you compare it to a p-series?

 

[dangish]

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

 

[jbunniii]

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?

 

[dangish]

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.

 

[jbunniii]

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

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.

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

 

[dangish]

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

 

[dangish]

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

 

[jbunniii]

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