Chapter 7: Q. 37 (page 640)
In Exercises 35–40 use the root test to analyze whether the given series converges or diverges. If the root test is inconclusive, use a different test to analyze the series.
Short Answer
The given series converges.
Chapter 7: Q. 37 (page 640)
In Exercises 35–40 use the root test to analyze whether the given series converges or diverges. If the root test is inconclusive, use a different test to analyze the series.
The given series converges.
All the tools & learning materials you need for study success - in one app.
Get started for freeUse either the divergence test or the integral test to determine whether the series in Given Exercises converge or diverge. Explain why the series meets the hypotheses of the test you select.
Use any convergence test from this section or the previous section to determine whether the series in Exercises 31–48 converge or diverge. Explain how the series meets the hypotheses of the test you select.
Let 0 < p < 1. Evaluate the limit
Explain why we cannot use a p-series with 0 < p < 1 in a limit comparison test to verify the divergence of the series
Provide a more general statement of the integral test in which the function f is continuous and eventually positive, and decreasing. Explain why your statement is valid.
An Improper Integral and Infinite Series: Sketch the function for x ≥ 1 together with the graph of the terms of the series Argue that for every term of the sequence of partial sums for this series,. What does this result tell you about the convergence of the series?
What do you think about this solution?
We value your feedback to improve our textbook solutions.