# Sufficient conditions to ensure divergence of a sequence in Maxima

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, ...