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Chapter 7: Q. 5 (page 655)
Fill in the blanks to complete each of the following theorem statements.
Basic Limit Rules for Convergent Sequences: If and if c is any constant, then
The required answer is
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Explain why, if n is an integer greater than 1, the series diverges.
Use either the divergence test or the integral test to determine whether the series in Given Exercises converge or diverge. Explain why the series meets the hypotheses of the test you select.
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
Use either the divergence test or the integral test to determine whether the series in Exercises 32鈥�43 converge or diverge. Explain why the series meets the hypotheses of the test you select.
35.
Find the values of x for which the series converges.
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