'Alternating harmonic series' presentation slideshows

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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Magical Math Results

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Section 9.8 and 9.9: Power Series

Section 9.8 and 9.9: Power Series. A Polynomial Series. Consider the Polynomial Series:. Investigate the partial sums of the sequence and compare the results to on a graph. Window: and . A Polynomial Series. Consider the Polynomial Series:.

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Infinite Sequences and Series

Infinite Sequences and Series. 8. Other Convergence Tests. 8.4. Alternating Series. Alternating Series. An alternating series is a series whose terms are alternately positive and negative. Here are two examples:

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The Ratio Test:

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Absolute vs. Conditional Convergence

Absolute vs. Conditional Convergence. Alternating Series and the Alternating Series Test. Series with Positive Terms. Recall that series in which all the terms are positive have an especially simple structure when it comes to convergence. .

809 views • 10 slides