Problems: Sequences and Series and Their Applications

In this chapter, the basic and advanced problems of sequences and series as well as their applications are presented. The subjects include limit of general term of a sequences and series, convergence or divergence status of a sequences and series, convergence range and radius of series, Maclaurin expansion, Taylor expansion, concept of growth rate, concept of equivalent functions, P-series, harmonic series, telescoping series, and Stirling’s approximation. In this chapter, the problems are categorized in different levels based on their difficulty levels (easy, normal, and hard) and calculation amounts (small, normal, and large). Additionally, the problems are ordered from the easiest problem with the smallest computations to the most difficult problems with the largest calculations.