Chapter 7: Q. 37 (page 615)
Evaluate the finite sums.
Short Answer
The sum of the seriesis,.
Chapter 7: Q. 37 (page 615)
Evaluate the finite sums.
The sum of the seriesis,.
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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.
For each series in Exercises 44–47, do each of the following:
(a) Use the integral test to show that the series converges.
(b) Use the 10th term in the sequence of partial sums to approximate the sum of the series.
(c) Use Theorem 7.31 to find a bound on the tenth remainder,.
(d) Use your answers from parts (b) and (c) to find an interval containing the sum of the series.
(e) Find the smallest value of n so that
In Exercises 48–51 find all values of p so that the series converges.
Ifconverges, explain why we cannot draw any conclusions about the behavior of.
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.
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