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Chapter 7: Q. 13 (page 603)
Give examples of sequences satisfying the given conditions or explain why such an example cannot exist.
A convergent sequence that is not eventually monotonic.
Examples of the sequences is .
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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.
The contrapositive: What is the contrapositive of the implication 鈥淚f A, then B.鈥�?
Find the contrapositives of the following implications:
If a quadrilateral is a square, then it is a rectangle.
For each series in Exercises 44鈥�47, do each of the following:
(a) Use the integral test to show that the series converges.
(b) Use the 10th term in the sequence of partial sums to approximate the sum of the series.
(c) Use Theorem 7.31 to find a bound on the tenth remainder, .
(d) Use your answers from parts (b) and (c) to find an interval containing the sum of the series.
(e) Find the smallest value of n so that localid="1649224052075" .
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.
Prove Theorem 7.24 (a). That is, show that if c is a real number and is a convergent series, then .
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