Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the series with an error of less than 0.0001. 5 (-1)" + 1 7n3 – 4 n = 1
Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the series with an error of less than 0.0001. 5 (-1)" + 1 7n3 – 4 n = 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the series with an error of less than 0.0001.
\[
\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{7n^3 - 4}
\]
In this expression, we have an alternating series. The goal is to find how many terms, \( n \), are needed so that the error in approximating the sum of the series is less than 0.0001. This involves applying the Alternating Series Remainder Theorem, which can help determine the required number of terms by checking the absolute value of the \( (n+1) \)-th term of the series. If this value is less than the desired error, the approximation is within the specified tolerance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7da64f87-97a6-4ade-9565-5d171f68500b%2F1d8d57b0-d696-4866-9374-20aa9ab48f19%2Ffjarmt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the series with an error of less than 0.0001.
\[
\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{7n^3 - 4}
\]
In this expression, we have an alternating series. The goal is to find how many terms, \( n \), are needed so that the error in approximating the sum of the series is less than 0.0001. This involves applying the Alternating Series Remainder Theorem, which can help determine the required number of terms by checking the absolute value of the \( (n+1) \)-th term of the series. If this value is less than the desired error, the approximation is within the specified tolerance.
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