Professor Ditmarr 3B 10.6 40: Show work finding the number of terms required. You may use technology for Calculation of sum. 39-44. Estimating infinite series Estimate the value of the following convergent series with an absolute error less than 10-3. $$40. \sum_{k=1}^{\infty} \frac{(-1)^k}{(2k+1)^3}$$
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The Alternating Series Estimation Theorem states that the error in approximating the sum of an alternating series by the sum of its first n terms is less than or equal to the absolute value of the (n+1)-th term. We want to find the number of terms n such that the Show more…
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Finding the Number of Terms In Exercises 35-40, use Theorem 9.15 to determine the number of terms required to approximate the sum of the series with an error of less than 0.001. $$\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^{3}}$$
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