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Chapter 7: Q. 11 (page 614)
Explain why all the terms of a divergent geometric series are nonzero.
The terms of a divergent geometric series are nonzero because if any one of the term is zero, then the series will be convergent.
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Determine whether the series converges or diverges. Give the sum of the convergent series.
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.
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
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