Convergence of a series

[502065]

I have a calculus test coming up next week and I won't lie, I am completely lost on how to tell what tests to use and when, other than just trying them all and hoping for the right answer. I have a few homework questions that I'm not sure what tests to use.
1. 1/ln(n+1)
2. 1/n(ln(n))^2

I know I should use the direct comparison test on the first one because my teacher told us to use that one but I don't know what to compare it to. Once I know that I can figure out the rest. and on the second one, I don't know what test to use or how to tell..

 

[tkhunny]

For the Second, n > 4, \(\displaystyle \left(ln(n)\right)^{2} > \sqrt{n}\)

For the First, n > 0, x > ln(x+1)

That should do it.

 

[lookagain]

\(\displaystyle For\ the \ second, \ n \ > \ 4, \ \left(ln(n)\right)^{2} \ > \ \sqrt{n}\)

\(\displaystyle For \ the \ first, \ n \ > \ 0, \ n \ > \ ln(n + 1)\)

Referring to the edited bottom line shown in the above quote box, tkhunny accidentally typed
something that was intended for the variables to be the same, and more specifically, to be in
terms of n.

 

[tkhunny]

Very true. Missed that.