Chapter 9.4 COMPARISONS OF SERIES.

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Presentation transcript:

Chapter 9.4 COMPARISONS OF SERIES

After you finish your HOMEWORK you will be able to… Us e the Direct Comparison Test to determine whether a series converges or diverges Use the Limit Comparison Test to determine whether a series converges or diverges.

THEOREM 9.12 DIRECT COMPARISON TEST Condition: Let 1. If converges, then converges. If diverges, then diverges.

USING THE DIRECT COMPARISON TEST Determine the convergence or divergence of Hmm…what series looks similar to this one?

You got it! It is similar to the geometric series Now we need to check if For n = 1, we get , n = 2 we get Can we use the test?

Yes! Conclusion: Since is a geometric series with which fulfills the condition , it converges (Thm. 9.6), so it follows that also converges by the direct comparison test (Thm. 9.12).

THEOREM 9.13 LIMIT COMPARISON TEST Condition: Let Where is finite and positive. Then the two series and either both converge or both diverge.