Chapter 7: Q. 1TF (page 641)
A series of monomials: Find all values of x for which the series converges.
a
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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
Prove Theorem 7.31. That is, show that if a function a is continuous, positive, and decreasing, and if the improper integral converges, then the nth remainder, , for the series is bounded by
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.
For a convergent series satisfying the conditions of the integral test, why is every remainder positive? How can be used along with the term from the sequence of partial sums to understand the quality of the approximation ?
What is meant by a p-series?
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