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: 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, ...


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