Use Theorem Alternating Series remainder to determine the number of terms required to approximate the sum of the series with an error of less than 0.001. ∑n=1∞(−1)n+1n5

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Use Theorem Alternating Series remainder to determine the number of terms required to approximate the sum of the series with an error of less than 0.001.  ∑n=1∞(−1)n+1n5

escumantsu · Accepted Answer

Given that ∑n=1∞(−1)n+1n5 We need use theorem alternating series to determine the number of terms requires to approximate the sum of the series with an error of less than 0.001. Given series is alternate series with an=1n5 We know that |Rn|≤aN+1=1(N+1)5 for an error less than 0.001N must satisfy the inequality. 1(N+1)5&amp;lt;0.001 10.001&amp;lt;(N+1)51000&amp;lt;(N+1)5 taking 15 root on both sides 100015 3.98  2.98 So we will need at least 4 terms to get an error less than 0.001

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Use Theorem Alternating Series remainder 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}^inftyfrac{(-1)^{n+1}}{n^5}

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