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 freeDetermine whether the series converges or diverges. Give the sum of the convergent 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.
Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.
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 localid="1649224052075" .
Explain why, if n is an integer greater than 1, the series diverges.
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