Remainders in alternating series Determine how

Chapter 10, Problem 29E

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QUESTION:

25-34. Remainders in alternating series Determine how many terms of the following convergent series must be summed to be sure that the remainder is less than \(10^{-4}\). Although you do not need it, the exact value of the series is given in each case.

\(\frac{7 \pi^{4}}{720}=\sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{k^{4}}\)

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QUESTION:

25-34. Remainders in alternating series Determine how many terms of the following convergent series must be summed to be sure that the remainder is less than \(10^{-4}\). Although you do not need it, the exact value of the series is given in each case.

\(\frac{7 \pi^{4}}{720}=\sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{k^{4}}\)

ANSWER:

SOLUTION

Step 1

We have to  determine how many terms of the following convergent series must be summed to be sure that the remainder is less than

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