Chapter 7: Q. 8 (page 614)
What is a geometric progression? What determines the
convergence of a geometric progression?
The series which is obtained by multiplying the terms by a fixed number is geometric progression.
The convergence of the geometric progression depends upon the common ratio.
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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 localid="1649224052075" .
Determine whether the series converges or diverges. Give the sum of the convergent series.
Ifconverges, explain why we cannot draw any conclusions about the behavior of.
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.
Prove Theorem 7.25. That is, show that the series either both converge or both diverge. In addition, show that if converges to L, thenconverges tolocalid="1652718360109"
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