Use the comparison test: From 1 to infinity 9/(7+8n (ln (n)^2))

[tjn014]

[h=1]Use the limit comparison test to determine if the series converges or diverges From 1 to infinity 9/(7+8n (ln (n)^2))?[/h]

 

[Deleted member 4993]

Use the limit comparison test to determine if the series converges or diverges From 1 to infinity 9/(7+8n (ln (n)^2))?

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

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[tjn014]

My first idea would be to take out the factor out the nine and change ln(n)^2 to 2ln(n) getting 1 to infinity of 9(1/8n*2ln(n)+7). this is the part that i am stuck on. I am not to sure what to compare it to. I dont think it would be 1/n because it diverges and the original problem would converge but i dont know how to show it. Could i compare it to 1/n^2? Sorry its my first time on here.

 

[tjn014]

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

my first idea would be to change it to 1 to infinity of 9(1/8n*ln(n)+7). Now this is that part i dont really understand, what would i compare it to? The only thing i could think of is 1/n, but 1/n diverges and i know the series converges. So the limit test wouldn't work correct? Could i compare it to 1/n^2? and sorry its my first time using this.

 

[Steven G]

My first idea would be to take out the factor out the nine and change ln(n)^2 to 2ln(n) getting 1 to infinity of 9(1/8n*2ln(n)+7). this is the part that i am stuck on. I am not to sure what to compare it to. I dont think it would be 1/n because it diverges and the original problem would converge but i dont know how to show it. Could i compare it to 1/n^2? Sorry its my first time on here.

How would what you have compare to what you have if you removed the 1/n or the 1/(ln(n))? Can you then do a comparison test to the modified faction?

 

[Steven G]

Use the limit comparison test to determine if the series converges or diverges From 1 to infinity 9/(7+8n (ln (n)^2))?

Are you supposed to use the comparison test, the limit comparison test (YOU listed both) or are you supposed to use both?? Be clear in stating your problem.

 

[tjn014]

Are you supposed to use the comparison test, the limit comparison test (YOU listed both) or are you supposed to use both?? Be clear in stating your problem.

I am suppose to use the limit comparison test, I guess i might be getting the two confused but woundnt you have to find another function to compare it to to get lim n to infinity of the original function another function? (an/bn)

 

[lookagain]

My first idea would be to take out the factor out the nine and change ln(n)^2 to 2ln(n) getting 1 to infinity of 9(1/8n*2ln(n)+7).

The way you have written it, ln(n)^2 = [ln(n)]^2, not ln(n^2) = 2*ln(n).

So, you cannot change it to what you think you can.