Chapter 7: Q. 84 (page 616)
Prove Theorem 7.24 (a). That is, show that if c is a real number and is a convergent series, then .
Short Answer
As is a convergent series, and c is constant we get c out of the summation and we prove that .
Chapter 7: Q. 84 (page 616)
Prove Theorem 7.24 (a). That is, show that if c is a real number and is a convergent series, then .
As is a convergent series, and c is constant we get c out of the summation and we prove that .
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Get started for freeLet f(x) be a function that is continuous, positive, and decreasing on the interval such that , What can the integral tells us about the series ?
Let f(x) be a function that is continuous, positive, and decreasing on the interval such that role="math" localid="1649081384626" . What can the divergence test tell us about the series ?
Determine whether the series converges or diverges. Give the sum of the convergent series.
Improper Integrals: Determine whether the following improper integrals converge or diverge.
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" .
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