Representing Functions by Power Series

A power series is said to represent a function f with a domain equal to the interval I of convergence of the series if the series converges to f(x) at that interval. That’s if:

Example

Theorem

Examples

Example(1)

We notice that And we know that:

Solution

Example(2)

We notice that And we know that:

Solution

Approximating ln2

Example(3)

We notice that And we know that:

Solution

Approximating arctan (0.5)

Showing that this series converges to e

Approximating e

Question Approximate 3 √e

Homework