Lecture 29 (Binomial Series)

Lecture 29 (Binomial Series) - Wednesday, March 14 Lecture...

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Unformatted text preview: Wednesday, March 14 Lecture 29 : Binomial series (Refers to Section 8.8 in your text) After having practiced the problems associated to the concepts of this lecture the student should be able to : State and apply the Binomial series theorem. 29.1 Introduction Recall the Binomial theorem, a theorem which most students have studied in high school: If n is a positive integer then where ( , ) = = ! ( )! ! We will study the Binomial series , a generalization of the expression ( + ) . 29.1.1 Definition Let be any real number and k be a non-negative integer. We define C ( , k ) as follows: ( , 0) = = 1 ( , ) = = ( 1)( 2)( 3) ( k + 1) ! 29.1.2 Example By C (1/3 , 5) we mean 1 3 , 5 = 1 3 5 = 1 3 1 3 1 1 3 2 ( 1 3 3) 1 3 5 + 1 5! By C ( 1/3 , 5) we mean 1 3 , 5 = 1 3 5 = 1 3 ( 1 3 1) 1 3 2 1 3 3 1 3 5 + 1 5! 29.2 Theorem The Binomial series theorem . Suppose is any real number. Then is any real number....
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This note was uploaded on 04/01/2012 for the course MATH 118 taught by Professor Zhou during the Winter '08 term at Waterloo.

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Lecture 29 (Binomial Series) - Wednesday, March 14 Lecture...

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