Dear Christopher Sangwin,
I really appreciate you very much. I expect my students can use comparison and limit comparison test to test the convergence or divergence for some nontrivial problems, but I find that Maxima is not good at not solving such kind of problem, for example, why I type "integrate(1/(1+log(x), x, 0,1);" Maxima does not seem to know it diverges.
Now, I shall consider your suggestion. Thank you very much again.
Best Wishes
C. T. Shieh