Sequences & Series

Sequences and series study ordered lists of numbers and the sums formed from them. This topic covers arithmetic and geometric sequences, convergence tests for infinite series, power series representations, and Taylor series expansions that approximate functions with polynomials.

Series are used in finance for computing compound interest and loan payments, in physics for solving differential equations via power series, and in computing for algorithm efficiency analysis.

Practice Tips

• 1For arithmetic sequences, always identify the first term and common difference; for geometric sequences, find the first term and common ratio.
• 2When testing series convergence, start with the divergence test (if the terms do not approach zero, the series diverges) before applying more advanced tests.
• 3Build Taylor series by computing derivatives at the expansion point and recognizing patterns in the coefficients rather than memorizing every formula.