1. MACLAURIN SERIES
how to represent certain types of functions as sums of power series
You might wonder why we would ever want to express a known function as a sum of infinitely many terms.
Integration. (Easy to integrate polynomials)
Finding limit
Finding a sum of a series (not only geometric, telescoping)

2. MACLAURIN SERIES
Example:
Maclaurin series ( center is 0 )
Example:
Find Maclaurin series

3. MACLAURIN SERIES
Important Maclaurin Series and Their Radii of Convergence
MEMORIZE: ** Students are required to know the series listed in Table 10.1, P. 620

4. MACLAURIN SERIES
Maclaurin series ( center is 0 )
Example:
Find Maclaurin series

5. MACLAURIN SERIES
TERM-081

6. MACLAURIN SERIES
TERM-091

7. MACLAURIN SERIES
TERM-101

8. MACLAURIN SERIES
TERM-082

9. MACLAURIN SERIES
TERM-102

10. MACLAURIN SERIES
TERM-091

11. TAYLOR AND MACLAURIN
Maclaurin series ( center is 0 )
Example:
Find the sum of the series

12. MACLAURIN SERIES
TERM-102

13. MACLAURIN SERIES
TERM-082

14. MACLAURIN SERIES
Example:
Find the sum
Leibniz’s formula:

15. MACLAURIN SERIES
Important Maclaurin Series and Their Radii of Convergence
MEMORIZE: ** Students are required to know the series listed in Table 10.1, P. 620

16. Example: MACLAURIN SERIES
Important Maclaurin Series and Their Radii of Convergence
Example:
Find Maclaurin series

17. MACLAURIN SERIES
TERM-102

18. MACLAURIN SERIES
TERM-111

19. MACLAURIN SERIES
TERM-101

20. MACLAURIN SERIES
TERM-082

21. MACLAURIN SERIES
Important Maclaurin Series and Their Radii of Convergence
MEMORIZE: ** Students are required to know the series listed in Table 10.1, P. 620