Chapter 7: Q. 15 (page 624)
Find an example of a continuous function f :such that diverges and localid="1649077247585" converges.
Short Answer
An example is.
Chapter 7: Q. 15 (page 624)
Find an example of a continuous function f :such that diverges and localid="1649077247585" converges.
An example is.
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Get started for freeLet f(x) be a function that is continuous, positive, and decreasing on the interval such that , What can the integral tells us about the series ?
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 .
Determine whether the series converges or diverges. Give the sum of the convergent series.
Determine whether the series converges or diverges. Give the sum of the convergent series.
Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.
(a) A divergent series in which .
(b) A divergent p-series.
(c) A convergent p-series.
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