Chapter 7: Q 19. (page 631)
In Example 1 we used the comparison test to show that the series converges. Use the limit comparison test to prove the same result.
Chapter 7: Q 19. (page 631)
In Example 1 we used the comparison test to show that the series converges. Use the limit comparison test to prove the same result.
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Let 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 ?
Determine whether the series converges or diverges. Give the sum of the convergent series.
Use either the divergence test or the integral test to determine whether the series in Exercises 32–43 converge or diverge. Explain why the series meets the hypotheses of the test you select.
37.
Let be a continuous, positive, and decreasing function. Complete the proof of the integral test (Theorem 7.28) by showing that if the improper integral converges, then the series localid="1649180069308" does too.
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