Thread: infinite series--integral?

Hi, I am supposed to determine whether "the sum of the sequence a(n)from n=1 to n=infinity" converges (i.e. whether or not the sequence is summable) where a(n)=1/[n^(1+(1/n)]. I figure I can use the fact that this sequence is summable if lim(A->infinity)[integral from 1 to A of f(x)] exists where f(x)=1/[x^(1+(1/x))]. My problem is I forget (or maybe never knew) how to find this integral which I must do to find the limit of the integral as A approaches infinity. Am I even approaching the question in the correct way?

Thankyou for any help

Once You have the explicit expressione for the , finding the integral for the covergence test is very easy: You have only to swap the and the ...

In Your example...

(1)

Kind regards

Originally Posted by chisigma

Once You have the explicit expressione for the , finding the integral for the covergence test is very easy: You have only to swap the and the ...

In Your example...

(1)

Kind regards

Thankyou for assuring me that I am going in the right direction with the integral test. I know I have to swap the n and the x and find the integral of (1) but my question is how do I do that? I can't use integration by parts because logx is missing from the equation (the derivative of 1+ 1/x would be logx right?) so I don't know how to integrate this.