Chapter 7: Q. 8 (page 655)
Some Convergent Sequences Involving Exponents: For any real number p > 0, the following sequences converge. Fill in each blank with the appropriate value.
Short Answer
The required answer is
Chapter 7: Q. 8 (page 655)
Some Convergent Sequences Involving Exponents: For any real number p > 0, the following sequences converge. Fill in each blank with the appropriate value.
The required answer is
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Get started for freeUse 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.
Let 0 < p < 1. Evaluate the limit
Explain why we cannot use a p-series with 0 < p < 1 in a limit comparison test to verify the divergence of the series
Explain why the integral test may be used to analyze the given series and then use the test to determine whether the series converges or diverges.
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"
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