Chapter 7: Q. 39 (page 615)
Evaluate the finite sums.
.
Short Answer
The sum of the seriesis,.
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Chapter 7: Q. 39 (page 615)
Evaluate the finite sums.
.
The sum of the seriesis,.
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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.
36.
Find the values of x for which the series converges.
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.
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.
Express each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.
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