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Chapter 7: Q. 12 (page 656)
Geometric Series and p-series:
Suppose r is a nonzero real number and p > 0. Fill in the blanks.
For p______ , the p-series converges and for p______, the series diverges.
The required answer is for p>1 , the p-series converges and for p<1, the series diverges.
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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.
Explain how you could adapt the integral test to analyze a series in which the function is continuous, negative, and increasing.
Express each of the repeating decimals in Exercises 71鈥�78 as a geometric series and as the quotient of two integers reduced to lowest terms.
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鈥�43 converge or diverge. Explain why the series meets the hypotheses of the test you select.
37.
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