'Alternating series estimation theorem' diaporamas de présentation

INFINITE SEQUENCES AND SERIES

11. INFINITE SEQUENCES AND SERIES. INFINITE SEQUENCES AND SERIES. 11.11 Applications of Taylor Polynomials. In this section, we will learn about: Two types of applications of Taylor polynomials. APPLICATIONS IN APPROXIMATING FUNCTIONS.

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SECTION 8.4

SECTION 8.4. OTHER CONVERGENCE TESTS. INFINITE SEQUENCES AND SERIES. The convergence tests that we have looked at so far apply only to series with positive terms. In this section we learn how to deal with series whose terms are not necessarily positive. ALTERNATING SERIES.

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INFINITE SEQUENCES AND SERIES

11. INFINITE SEQUENCES AND SERIES. INFINITE SEQUENCES AND SERIES. The convergence tests that we have looked at so far apply only to series with positive terms. INFINITE SEQUENCES AND SERIES. 11.5 Alternating Series. In this section, we will learn: How to deal with series

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ALTERNATING SERIES

ALTERNATING SERIES. series with positive terms. series with some positive and some negative terms. alternating series. n-th term of the series. are positive. ALTERNATING SERIES. alternating series. alternating harmonic series. alternating geomtric series. alternating p-series.

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Infinite Sequences and Series

Infinite Sequences and Series. 8. Applications of Taylor Polynomials. 8.8. Applications of Taylor Polynomials.

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Infinite Sequences and Series

Infinite Sequences and Series. 8. Applications of Taylor Polynomials. 8.8. Applications of Taylor Polynomials.

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Testing Convergence At Endpoints

Testing Convergence At Endpoints. Section 11.5. Integrate. converges if , diverges if . p-series Test.

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Review of Tests for Series

Review of Tests for Series. If , then both and converge or both diverge. Limit Comparison Test. If and for all ( N a positive integer).

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9.5 Testing Convergence at Endpoints

Photo by Vickie Kelly, 2007. Greg Kelly, Hanford High School, Richland, Washington. 9.5 Testing Convergence at Endpoints. Petrified Forest National Park, Arizona. If is a series with positive terms and. then:. The series converges if .

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9.5 Testing Convergence at Endpoints

9.5 Testing Convergence at Endpoints. Petrified Forest National Park, Arizona. If is a series with positive terms and. then:. The series converges if. The series diverges if. The test is inconclusive if. Remember:. The Ratio Test :.

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Testing Convergence at Endpoints

Photo by Vickie Kelly, 2007. Greg Kelly, Hanford High School, Richland, Washington. Testing Convergence at Endpoints. Petrified Forest National Park, Arizona. If is a series with positive terms and. then:. The series converges if. The series diverges if.

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9.5 Testing Convergence at Endpoints

Photo by Vickie Kelly, 2007. Greg Kelly, Hanford High School, Richland, Washington. 9.5 Testing Convergence at Endpoints. Petrified Forest National Park, Arizona. If is a series with positive terms and. then:. The series converges if. The series diverges if.

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Alternating Series

Alternating Series. The last special type of series that AP requires is alternating series. A series is alternating if every other term is positive and every other term is negative.

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2 3 1

The following table contains the evaluation of the Taylor polynomial centered at a = 1 for f(x) = 1/ x . What is the degree of this polynomial? x T(x) 0.5 1.88 0.6 1.62 1.8 0.33 2.9 -4.15 3 -5.00. 2 3 1. 1. 2. 3.

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10.6 Alternating Series

10.6 Alternating Series. Math 6B Calculus II. Alternating Series Theorem. Estimating Sums. Alternating Series Estimation Theorem. Absolute and Conditional Convergence. A series is called absolutely convergent if the series of absolute values is convergent.

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