Chapter 7: Q. 13 (page 656)
Convergence Tests for Series: Fill in the blanks.
The Divergence Test: If the sequence does not converge to ____, then the series__.
Short Answer
If the sequence does not converge to 0, then the series diverges.
Chapter 7: Q. 13 (page 656)
Convergence Tests for Series: Fill in the blanks.
The Divergence Test: If the sequence does not converge to ____, then the series__.
If the sequence does not converge to 0, then the series diverges.
All the tools & learning materials you need for study success - in one app.
Get started for freeIn Exercises 48–51 find all values of p so that the series converges.
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.
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.
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.
True/False:
Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.
(a) True or False: If , then converges.
(b) True or False: If converges, then .
(c) True or False: The improper integral converges if and only if the series converges.
(d) True or False: The harmonic series converges.
(e) True or False: If , the series converges.
(f) True or False: If as , then converges.
(g) True or False: If converges, then as .
(h) True or False: If and is the sequence of partial sums for the series, then the sequence of remainders converges to .
What do you think about this solution?
We value your feedback to improve our textbook solutions.