1/n^(1+1/n) Converge or diverge?

[runningeagle]

Hi

I am looking at

, that's 1/n^(1+1/n) from n=1 to infinity and seeing whether it converges or diverges.

The first test that I use is integral test. Terms are postive and decreasing, so it applies. But, how do I take the integral of this sequence? Is it [ln(n)-1-n]/n^(3+1/n)?

I cannot think of any series to compare with using Limit or Direct comparison tests.

Thank you.

 

[galactus]

The integral test is not a good choice for this one. The ratio test may be better.

The ratio test gives infinity. So, it diverges.

 

[Deleted member 4993]

Hi

I am looking at

, that's 1/n^(1+1/n) from n=1 to infinity and seeing whether it converges or diverges.

I cannot see the image - is it a series or sequence?

The first test that I use is integral test. Terms are postive and decreasing, so it applies. But, how do I take the integral of this sequence? Is it [ln(n)-1-n]/n^(3+1/n)?

I cannot think of any series to compare with using Limit or Direct comparison tests.

Thank you.

 

[runningeagle]

It is the SERIES of 1/n^(1+1/n) from n=1 to infinity.

I get 1 when doing the ratio test. I am sure I screwed up on algebra somewhere.Can you explain the steps from here?[attachment=0:2tmqtlkz]ratiotest.jpg[/attachment:2tmqtlkz]