Solution Found!
Remainders in alternating series Determine how
Chapter 10, Problem 29E(choose chapter or problem)
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.
\(\frac{7 \pi^{4}}{720}=\sum_{k=1}^{\infty} \frac{(-1)^{k+1}}{k^{4}}\)
Questions & Answers
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