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)

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

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

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

MACLAURIN SERIES TERM-081

MACLAURIN SERIES TERM-091

MACLAURIN SERIES TERM-101

MACLAURIN SERIES TERM-082

MACLAURIN SERIES TERM-102

MACLAURIN SERIES TERM-091

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

MACLAURIN SERIES TERM-102

MACLAURIN SERIES TERM-082

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

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

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

MACLAURIN SERIES TERM-102

MACLAURIN SERIES TERM-111

MACLAURIN SERIES TERM-101

MACLAURIN SERIES TERM-082

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