Practical Session 6: Power Series Expansions and Applications

This practical session develops students' skills in working with Taylor and Maclaurin series through active problem-solving. The material is intended for students studying mathematical analysis who are familiar with power series concepts.

The session covers multiple approaches to finding series expansions: direct computation using derivatives, substitution into known series, integration of series, and application of the binomial series. Problems progress from basic Maclaurin series to Taylor series about nonzero points and series multiplication.

Applications of power series are explored through evaluating limits, approximating definite integrals without elementary antiderivatives, and error estimation using Taylor's Inequality. Each problem includes complete step-by-step solutions. The session concludes with homework problems and a summary of key formulas, including essential Maclaurin series to memorize.