1. Representing Functions by Power Series

2. 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:

3. Example

4. Theorem

5. Examples

6. Example(1)

7. We notice that And we know that:

8. Solution

9. Example(2)

10. We notice that And we know that:

11. Solution

12. Approximating ln2

14. Example(3)

15. We notice that And we know that:

17. Solution

18. Approximating arctan (0.5)

21. Showing that this series converges to e

23. Approximating e

24. Question Approximate 3 √e

25. Homework