'Series converges' diaporamas de présentation

Lecture 2

Lecture 2.

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Chapter 9

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Math 104 Calculus I

Math 104 Calculus I. SEQUENCES and INFINITE SERIES. Sequences. The lists of numbers you generate using a numerical method like Newton's method to get better and better approximations to the root of an equation are examples of (mathematical) sequences .

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(MTH 250)

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Asymptotic Series

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Visualizing The Direct Comparison Test for Infinite Series

Visualizing The Direct Comparison Test for Infinite Series. A Presentation by Pablito Delgado Sponsored by the Center for Academic Program Support (CAPS) University of New Mexico. Why Are We Doing This?. To make Calculus students suffer!!! Just kidding! :)

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Calculus II (MAT 146) Dr. Day Wednes day November 20, 2013

Calculus II (MAT 146) Dr. Day Wednes day November 20, 2013. Transforming Series into Functions Power Series Coefficients Applying the Ratio Test to Power Series Radius of Convergence Interval of Convergence Assignments and Announcements. Use the Ratio Test to Determine Convergence.

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Sec. 9.4: Comparisons of Series

Sec. 9.4: Comparisons of Series. Sec. 9.4: Comparisons of Series. The tests we have used so far involved either fairly simple series or series with special characteristics. Any deviation, no matter how slight, would render a test nonapplicable. Sec. 9.4: Comparisons of Series.

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Calculus II (MAT 146) Dr. Day Monday Nov 18, 2013

Calculus II (MAT 146) Dr. Day Monday Nov 18, 2013. Series Convergence Tests: Practice and Reflect Using Series to Re-Express Functions! Assignments and Announcements. Converge or Diverge?. Converge or Diverge?. Converge or Diverge?. Determine Convergence or Divergence.

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Radius of convergence

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Section 8.7: Power Series

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DEFINITION Absolute Convergence

In the previous section, we studied positive series, but we still lack the tools to analyze series with both positive and negative terms. One of the keys to understanding such series is the concept of absolute convergence. DEFINITION Absolute Convergence. Verify that the series.

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Warm Up

Warm Up. Write the explicit formula for the series. Evaluate. Introduction to Series. What is a series? What does it mean for a series to converge? What are geometric and telescoping series? What is the nth term test?. Infinite Series. Partial Sums.

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Alternating Series

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Positive Series:

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Nth term & Alternating Series

Nth term & Alternating Series. Dean Lee & Jenny Park AP Calculus BC G Block 9/2/2011. Practice Problems. Does the series converge? . 1. 2 . (Harmonic Series). 3 . Nth term Test. Requirement for convergence of a series nth term approaches 0 as n -> infinity

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9.4 Comparisons of Series

9.4 Comparisons of Series. Direct Comparison Test. This series converges. For non-negative series:. So this series must also converge. If every term of a series is less than the corresponding term of a convergent series, then both series converge. So this series must also diverge.

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The Direct Comparison Test (Note: all terms must be positive)

The Direct Comparison Test (Note: all terms must be positive). Part 1 The series diverges if there exists another series such that b n < a n and b n diverges, then the series diverges. Part 2 The series converges if there exists another

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