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Power Series

Power Series . An important function f ( x ) = e x can be represented exactly by an infinite series called a power series. For example, the power series representation for e x is

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Power Series

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  1. Power Series An important function f(x) = ex can be represented exactly by an infinite series called a power series. For example, the power series representation for ex is For each real number x, it can be shown that the infinite series on the right converges to the number ex.

  2. Example 1 – Power Series a. The following power series is centered at 0. b. The following power series is centered at –1. c. The following power series is centered at 1.

  3. Radius and Interval of Convergence

  4. Differentiation and Integration of Power Series

  5. Taylor Series and Maclaurin Series

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