Series comparison test question

[cue928]

Homework Statement

Summation from n=1 to infinity: (e^(1/n)) / n

Homework Equations

The Attempt at a Solution

Can someone point out what criteria I should be considering when trying to determine which test to use? I was looking at a comparison test as a way to go on this one. I'd chosen an = (e^(1/n))/n and bn = 1/n. Since bn is a divergent p-series then an should also be divergent. Am I on the right track there?

 

[Dick]

Yes. an>bn, right?

 

[cue928]

Yes, just testing out the first few terms, yes, an>bn, so the series an is divergent.

 

[Dick]

Yes, just testing out the first few terms, yes, an>bn, so the series an is divergent.

You might want to try to give a better reason why e^(1/n)>1 than just testing the first few terms.