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Chapter 7: Q. 71 (page 654)

Changing the order of the summands in a conditionally convergent series can change the value of the sum. We showed this earlier in the section for the alternating harmonic series

Short Answer

Expert verified

Hence, the series is divergent.

Step by step solution

Step 1. Given information

Changing the order of the summands in a conditionally convergent series can change the value of the sum.

Step 2. Proof

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Most popular questions from this chapter

Prove Theorem 7.31. That is, show that if a function a is continuous, positive, and decreasing, and if the improper integral $\int_{1}^{\infty} a (x) d x$ converges, then the nth remainder, $R_{n}$ , for the series $\sum_{k = 1}^{\infty} a (k)$ is bounded by $0 \leq R_{n} = \sum_{k = n + 1}^{\infty} a (k) \leq \int_{n}^{\infty} a (x) d x$

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Changing the order of the summands in a conditionally convergent series can change the value of the sum. We showed this earlier in the section for the alternating harmonic series

Short Answer

Step by step solution

Step 1. Given information

Step 2. Proof

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Most popular questions from this chapter

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