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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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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 is geometric, is not. is a p-series, is not. is easily integrated, is not.
Sec. 9.4: Comparisons of Series The next two tests allow you to compare a complicated series with a simpler series whose convergence or divergence is known.
Sec. 9.4: Comparisons of Series Since the convergence of a series is not dependent on the first several terms, you could modify the test to require only that 0 < an ≤ bn for all n greater than some integer N.
AP Calculus BCMonday, 31 March 2014 • OBJECTIVETSW (1) use the Direct Comparison Test (DCT) to determine whether a series converges or diverges, and (2) use the Limit Comparison Test (LCT) to determine whether a series converges or diverges. • CROSS-SECTION PROJECTS • Put on the table on the side with the purple rubrics sheet underneath (do not attach). • ASSIGNMENTS DUE • Sec. 9.1 wire basket • Sec. 9.2 black tray • Sec. 9.3 to the right of the black tray • QUIZ: Sec. 9.1 – 9.3 will be given after the lesson.
Sec. 9.4: Comparisons of Series 0 < an ≤ bn and 0 < bn ≤ an and converges diverges If a larger series converges, then the smaller series also converges. If a smaller series diverges, then the larger series also diverges.
Sec. 9.4: Comparisons of Series Ex: Determine the convergence or divergence of the following. Include these in your answer for all n≥ 1
Sec. 9.4: Comparisons of Series Ex: Determine the convergence or divergence of the following. for all n≥ 1 So no conclusion can be made using Try a different series.
Sec. 9.4: Comparisons of Series Ex: Determine the convergence or divergence of the following. Term-by-term comparison:
Sec. 9.4: Comparisons of Series Ex: Determine the convergence or divergence of the following. When a different N value is used, be sure to state it.
QUIZ: Sec. 9.1 – 9.3 • You may use a calculator.
AP Calculus BCTuesday, 01 April 2014 • OBJECTIVETSW (1) use the Direct Comparison Test (DCT) to determine whether a series converges or diverges, and (2) use the Limit Comparison Test (LCT) to determine whether a series converges or diverges.
Sec. 9.4: Comparisons of Series Informally, the Direct Comparisons Test says – (1) If the larger series Σbn converges, then the smaller series Σan must also converge. (2) If the smaller series Σan diverges, then the larger series Σbn must also diverge.
Sec. 9.4: Comparisons of Series Limit Comparison Test The next test, the Limit Comparison Test, should be used when a term-by-term comparison would be cumbersome to show.
Sec. 9.4: Comparisons of Series and and converges diverges
Sec. 9.4: Comparisons of Series Ex:Given Series Comparison Series
Sec. 9.4: Comparisons of Series Ex: Determine the convergence or divergence of the following.
Sec. 9.4: Comparisons of Series Ex: Determine the convergence or divergence of the following.