Chapter 7: Q. 32 (page 592)
In Exercises 31–36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index 1.
Short Answer
The first five terms are
Chapter 7: Q. 32 (page 592)
In Exercises 31–36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index 1.
The first five terms are
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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 .
Let f(x) be a function that is continuous, positive, and decreasing on the interval such that role="math" localid="1649081384626" . What can the divergence test tell us about the series ?
Determine whether the series converges or diverges. Give the sum of the convergent 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.
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
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