Chapter 7: Q. 13 (page 656)
Convergence Tests for Series: Fill in the blanks.
The Divergence Test: If the sequence does not converge to ____, then the series__.
Short Answer
If the sequence does not converge to 0, then the series diverges.
Chapter 7: Q. 13 (page 656)
Convergence Tests for Series: Fill in the blanks.
The Divergence Test: If the sequence does not converge to ____, then the series__.
If the sequence does not converge to 0, then the series diverges.
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Get started for freeDetermine whether the series converges or diverges. Give the sum of the convergent series.
Prove Theorem 7.31. That is, show that if a function a is continuous, positive, and decreasing, and if the improper integral converges, then the nth remainder, , for the series is bounded by
Use either the divergence test or the integral test to determine whether the series in Exercises 32–43 converge or diverge. Explain why the series meets the hypotheses of the test you select.
36.
Prove Theorem 7.25. That is, show that the series either both converge or both diverge. In addition, show that if converges to L, thenconverges tolocalid="1652718360109"
Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.
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