Worked examples

Power series and Taylor series

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Radius and set of convergence with the ratio test
• 2Radius and set of convergence with the root test
• 3Complete study of the behavior at the endpoints
• 4Lacunary power series
• 5Maclaurin expansions by substitution and manipulation
• 6Expansions by term-by-term differentiation and integration
• 7Taylor series centered at a point other than the origin
• 8Sums of numerical series with the standard expansions