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Section10.3b-ConvergenceOfSeriesWithPositiveTerms

Section10.3b-ConvergenceOfSeriesWithPositiveTerms -...

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Section 10.3b Convergence of Series with Positive Terms
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Introduction 2 1 1 n n 1 1 n behaves like when n is large. Suspect divergence. 1 n 1 1 21 n n 1 n behaves like when n is large. Suspect convergence. 1 2 n
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Comparison Test n a Suppose that there exists M > 0 such that for n M. n b 0 nn ab i) If is convergent, then is also convergent. n b n a ii) If is divergent, then is also divergent. Note: 1) Both series must have non negative terms. 2) We only compare two series that converge or two series that diverge.
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Example 2 1 1 n n 1 1 n b n 1 n a n nn ab for all n 2 n a is a divergent p series, p = 1 > 1 2 n n b is divergent by CT (Comparison Test) both with positive terms
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Steps 1) Identify series to compare to. 2) Check criteria. 3) Execute test. 4) Show convergence results for comparison series. 5) State conclusion.
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Repeat Example 2 1 1 n n 1 1 n b n 1 n a n nn ab
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Section10.3b-ConvergenceOfSeriesWithPositiveTerms -...

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