I will be teaching Calculus 2 this fall at a large U.S. state university. Our incoming students tend to have a limited or inconsistent background, which limits the amount of material we can cover.
Previously at my university, instructors have given sequences and series a very thorough treatment, including all the usual tests for convergence (ratio, root, alternating series, comparison, integral, etc.). For lack of time, important subjects such as topics such as arc length, parametric equations, polar coordinates, etc. have had to be dropped or abbreviated. I want to cover these subjects, and therefore am looking for something else to cut.
It seems possible to give an abbreviated treatment of sequences and series: cover the basics, do only the Ratio Test, and then teach Taylor and Maclaurin series. The students will be able to determine the radius of convergence, although perhaps not the endpoints.
Have people tried this approach previously? And are there disadvantages to such an approach, apart from the ones which can be easily foreseen?