Chapter 7: Q. 4 (page 652)
Find an example of a divergent series of the form
(a) that satisfies conditions (i) and (iii), but not condition (ii);
(b) that satisfies conditions (i) and (ii), but not condition (iii).
Short Answer
(i)
Chapter 7: Q. 4 (page 652)
Find an example of a divergent series of the form
(a) that satisfies conditions (i) and (iii), but not condition (ii);
(b) that satisfies conditions (i) and (ii), but not condition (iii).
(i)
All the tools & learning materials you need for study success - in one app.
Get started for freeFor 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.
Whenever a certain ball is dropped, it always rebounds to a height60% of its original position. What is the total distance the ball travels before coming to rest when it is dropped from a height of 1 meter?
Express each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.
Use any convergence test from this section or the previous section to determine whether the series in Exercises 31–48 converge or diverge. Explain how the series meets the hypotheses of the test you select.
Given a series , in general the divergence test is inconclusive when . For a geometric series, however, if the limit of the terms of the series is zero, the series converges. Explain why.
What do you think about this solution?
We value your feedback to improve our textbook solutions.