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Chapter 7: Q. 16 (page 639)
Explain why the series converges. Which convergence tests could be used to prove this?
Hence proved.
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What is the contrapositive of the implication “If A, then B"?
Find the contrapositives of the following implications:
If a divides b and b dividesc, then a divides c.
Improper Integrals: Determine whether the following improper integrals converge or diverge.
Determine whether the series converges or diverges. Give the sum of the convergent series.
For each series in Exercises 44–47, 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.
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.
35.
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