Thread: Help With Series

Determine whether the series ∑_(n=1)^(infinity) ((squareroot(n)+ln(n))/((n^2)+1)) converges or diverges. clearly identigy any test(s) you are using and label all relevant data and/or properties.

I have no idead where to start or what tests to use.

It can be shown that

Can you then find a bound on each term of your series?


Hint - think comparison test and p-test to arrive at your final answer!

Originally Posted by benb89

It can be shown that

Can you then find a bound on each term of your series?


Hint - think comparison test and p-test to arrive at your final answer!

Are you saying compare it to squareroot(n)/n?

So,



Can you go forward from here?

NO!
.
The last is a p-series that converges.

Originally Posted by benb89

So,



Can you go forward from here?

I'm not sure. I'm using the comparison test right? Or could I use the limit comparison test?

Originally Posted by Plato

NO!
.
The last is a p-series that converges.

Oh! Okay. So am I going to have to do multiple comparison tests?

Originally Posted by Preston019

Oh! Okay. So am I going to have to do multiple comparison tests?

No you don't.
Just say converges.

Originally Posted by Plato

No you don't.
Just say converges.

Okay. And where did you get ln(n) is less than or equal to the square root of n?