T12_Sequences_Series_Binomial_Theorem

# T12_Sequences_Series_Binomial_Theorem - PMC 0045...

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Unformatted text preview: PMC 0045 Pre-Calculus for Engineering Foundation in Engineering ONLINE NOTES Topic 12 Sequences and Binomial Theorem FOSEE , MULTIMEDIA UNIVERSITY (436821-T) MELAKA CAMPUS, JALAN AYER KEROH LAMA, 75450 MELAKA, MALAYSIA. Tel 606 252 3594 Fax 606 231 8799 URL: http://fosee.mmu.edu.my/~asd/ Mathematics Department (MD) Centre for Foundation Studies and Extension Education (FOSEE) PMC0045 Pre-Calculus for Engineering Topic 12 TOPIC 12: SEQUENCES AND BINOMIAL THEOREM References : 1. Sullivan, M. (2002), Algebra & Trigonometry , 6 th Ed., Prentice Hall. 2. Blitzer, R., Goh Wei Wei, et.al. (2005), Algebra & Trigonometry , Prentice Hall. Objectives: 1. To recognize a sequence with the nth term. 2. To list the terms from and write a recursion formula. 3. To write a series with the summation notation. 4. To recognize an arithmetic sequence, and find the sum of the first n terms. 5. To recognize a geometric sequence, and find the sum of the first n terms. 6. To find the sum of an infinite geometric series. 7. Using the Binomial Theorem to expand ( a + b ) n Contents: 12.1 Sequences and Summation Notation 12.2 Arithmetic Sequences 12.3 Geometric Sequences 12.4 Mathematical Induction 12.5 The Binomial Theorem 12.1 SEQUENCES AND SUMMATION NOTATION A sequence is a function whose domain is the set of positive integers. Example: { } = n a n 1 Sequence: ,.. 5 , 4 , 3 , 2 , 1 ... 5 1 , 4 1 , 3 1 , 2 1 , 1 = n The Factorial Symbol If ≥ n is an integer, the factorial symbol is defined as follows: 0! = 1; 1! =1; n! = n.(n-1).(n-2)…3.2.1, if n 2 ≥ . Note : n! = (n).(n-1).(n-2)…3.2.1 n! = n..(n-1)! . Example: 6! = 6.5.4.3.2.1 = 720 7! = 7. 6! = 7. 720 = 5040 ______________________________________________________________________________________ Mathematics Dept 2/ 6 PMC0045 Pre-Calculus for Engineering Topic 12 Recursion Formulas To assign a value to the first few terms and specify the nth term by a formula or equation that involves one or more of the terms preceding it. - recursive formula....
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T12_Sequences_Series_Binomial_Theorem - PMC 0045...

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