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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Find the values of x for which the series converges.
Provide a more general statement of the integral test in which the function f is continuous and eventually positive, and decreasing. Explain why your statement is valid.
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.
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.
An Improper Integral and Infinite Series: Sketch the function for x ≥ 1 together with the graph of the terms of the series Argue that for every term of the sequence of partial sums for this series,. What does this result tell you about the convergence of the series?
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