Chapter 7: Q. 19 (page 615)
Find two divergent geometric series and with all positive terms such that converges.
Short Answer
Ans:
part (a). The divergent geometric series
part (b). The divergent geometric series
part (c). The series is converge
Chapter 7: Q. 19 (page 615)
Find two divergent geometric series and with all positive terms such that converges.
Ans:
part (a). The divergent geometric series
part (b). The divergent geometric series
part (c). The series is converge
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Get started for freeExpress each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.
Determine whether the series converges or diverges. Give the sum of the convergent series.
Find the values of x for which the series converges.
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 .
Which p-series converge and which diverge?
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