Chapter 7: Q. 19 (page 652)
Give an example of divergent series and such that the series role="math" localid="1649434191353" converges.
Short Answer
The seriesis convergent.
Chapter 7: Q. 19 (page 652)
Give an example of divergent series and such that the series role="math" localid="1649434191353" converges.
The seriesis convergent.
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Prove Theorem 7.25. That is, show that the series either both converge or both diverge. In addition, show that if converges to L, thenconverges tolocalid="1652718360109"
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 is the contrapositive of the implication “If A, then B"?
Find the contrapositives of the following implications:
If a divides b and b dividesc, then a divides c.
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.
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