Monday, Nov 2, 2015MAT 146 Next Test: Thurs 11/19 & Fri 11/20.

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Presentation transcript:

Monday, Nov 2, 2015MAT 146 Next Test: Thurs 11/19 & Fri 11/20

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146 We start with a sequence {a n }, n going from 1 to ∞, and define {s i } as shown. The {s i } are called partial sums. These partial sums themselves form a sequence. An infinite series is the summation of an infinite number of terms of the sequence {a n }.

Monday, Nov 2, 2015MAT 146 The harmonic series is the sum of all possible unit fractions.

Monday, Nov 2, 2015MAT 146 A geometric series is created from a sequence whose successive terms have a common ratio. When will a geometric series converge?

Monday, Nov 2, 2015MAT 146 A telescoping sum can be compressed into just a few terms.

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146 Our goal is to determine whether an infinite series converges or diverges. It must do one or the other. If the sequence of partial sums {s i } has a finite limit as n −−> ∞, we say that the infinite series converges. Otherwise, it diverges.

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146 On of our goals this chapter is to generate polynomial functions that can be used to approximate other functions near particular values of x. The polynomial we seek is of the following form:

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146

Monday, Nov 2, 2015MAT 146 Goal: Generate polynomial functions to approximate other functions near particular values of x. Create a third-degree polynomial approximator for

Monday, Nov 2, 2015MAT 146 Create a 3rd-degree polynomial approximator for

Monday, Nov 2, 2015MAT 146

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