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.
Regards
Niall101
If one finds the limits and they are finite then they converge. To find all the limits may not be what was intended but it is convincing and proves what was asked if not by the means intended.
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.
CB