Chapter 7: Q. 13 (page 639)
Explain how you could adapt the root test to analyze a seriesin which the terms of the series are all negative.
Short Answer
Hence proved.
Chapter 7: Q. 13 (page 639)
Explain how you could adapt the root test to analyze a seriesin which the terms of the series are all negative.
Hence proved.
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Get started for freeUse either the divergence test or the integral test to determine whether the series in Given Exercises converge or diverge. Explain why the series meets the hypotheses of the test you select.
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.
The contrapositive: What is the contrapositive of the implication “If A, then B.”?
Find the contrapositives of the following implications:
If a quadrilateral is a square, then it is a rectangle.
True/False:
Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.
(a) True or False: If , then converges.
(b) True or False: If converges, then .
(c) True or False: The improper integral converges if and only if the series converges.
(d) True or False: The harmonic series converges.
(e) True or False: If , the series converges.
(f) True or False: If as , then converges.
(g) True or False: If converges, then as .
(h) True or False: If and is the sequence of partial sums for the series, then the sequence of remainders converges to .
Use any convergence test from this section or the previous section to determine whether the series in Exercises 31–48 converge or diverge. Explain how the series meets the hypotheses of the test you select.
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