Your notation is not so clear.
Do you mean for example number 2 is showing the convergence/divergence of ?
So the series is divergent.
Asked to test the following for convergence using the comparason test as much as possible.
1. 1/(n^p-n^q) 0<q<p I thin kthe limit in this one does not exist but cant say why.
2. sqrt(N^2+1) - n
3. (n^(1/n) -1) I think this converges to a limit of -1 but cant show why
Please help I am totally stuck.
It also simplifies the process of testing if you know the answer (that is if they do or do not converge)
Also, at a number of points in my posts one can just use tests to check for convergence rather than proceed to actualy find the limits.