I am using Maxima to check whether a given sequence is diverging to $+\infty$.
I know that this problem is undecidable and we note that Maxima is throwing an error:
sum(1/i,i,1,inf); sum: sum is divergent. -- an error. Entering the Maxima debugger.
I still do not know how I can catch this error in maxima but this is not central.
I am interested in sufficient conditions that can be implemented via Maxima to ensure that a sequence is divergent. Even if these conditions are very restrictive, I could still use them but the important point is that they should be implementable in Maxima.
Conditions like :$(u_n)$ is strictly increasing, $(u_n)$ should be polynomial, ...