11_1 - index of summation 1 Rules of the summation • ∑ n k =1 ca k = c ∑ n k =1 a k • ∑ n k =1 c = c ∑ n k =1 1 = cn • ∑ n k =1 a k

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Section 11.1: Sequences Instructor: Ms. Hoa Nguyen ([email protected]) 1 Sequence Notations A sequence is a list of numbers. The notation is: { a n } = a 1 , a 2 , a 3 , ... . Each number is called a term of the sequence. Example 1 : Example 2 : A sequence can be defined recursively, i.e., except the given first term, each term of the sequence is defined by a formula involving the previous terms. Example 3 : 2 Summation The finite and infinite sums of a sequence { a n } : n k =1 a k = a 1 + a 2 + ... + a n k =1 a k = a 1 + a 2 + ... Note: k is called the
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Unformatted text preview: index of summation . 1 Rules of the summation • ∑ n k =1 ca k = c ∑ n k =1 a k • ∑ n k =1 c = c ∑ n k =1 1 = cn • ∑ n k =1 ( a k ± b k ) = ∑ n k =1 a k ± ∑ n k =1 b k • ∑ n k =1 a k = ∑ m k =1 a k + ∑ n k = m +1 a k where 1 < m < n . Important Sums • ∑ n k =1 k = n ( n +1) 2 • ∑ n k =1 k 2 = n ( n +1)(2 n +1) 6 • ∑ n k =1 k 3 = ( n ( n +1) 2 ) 2 Example 4 : Example 5 : 2...
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This note was uploaded on 05/23/2011 for the course MAC 1147 taught by Professor Nuegyen during the Spring '11 term at FSU.

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11_1 - index of summation 1 Rules of the summation • ∑ n k =1 ca k = c ∑ n k =1 a k • ∑ n k =1 c = c ∑ n k =1 1 = cn • ∑ n k =1 a k

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