Does this Divergence Test problem converge?

[flyintiger]

Hey guys, was wondering if anyone could help walk me through this problem. I am fairly sure it converges by the ratio test. Thank you.

http://www.wolframalpha.com/share/clip?f=d41d8cd98f00b204e9800998ecf8427e1sgqilv5iv

 

[Millennial]

What's wrong? Wolfram says it is convergent too.

 

[flyintiger]

Sorry, i just want to check the work. I am having some trouble convincing myself that it is correct. I keep getting that the ratio test is inconclusive (=1) so i need to see someone else work the problem.

 

[Millennial]

I do not know about the ratio test but the series surely converges by the Cauchy root test.

 

[flyintiger]

I've got it, but it's messy with the ratio test unless you imply some limits. Root test FTW!