Chapter 7: Q.19 (page 639)
explain why the ratio test cannot be used on the seriesthen show that the series converges and find its sum.
Short Answer
The required sum to converges the series is
Chapter 7: Q.19 (page 639)
explain why the ratio test cannot be used on the seriesthen show that the series converges and find its sum.
The required sum to converges the series is
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Get started for freeFor 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
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.
In Exercises 48–51 find all values of p so that the series converges.
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.
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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