How Many Terms Are Needed for 0.01 Accuracy in an Alternating Series?

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To achieve an accuracy of 0.01 for the alternating series ∑((-2)^n)/n!, the error estimate indicates that the first unused term provides a bound for the error. Specifically, the magnitude of the next term in the series must be less than 0.01 to ensure the desired accuracy. For this series, calculating the terms reveals that approximately 5 terms are needed to meet the accuracy requirement. The discussion emphasizes the importance of understanding error estimates in alternating series without relying on methods like Riemann, Trapezoidal, or Simpson. Overall, recognizing how to apply the error bound from the first unused term is crucial for solving such problems.
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Q: How many terms of the alternating series \sum((-2)^n)/n! needed to find the sum to an accuray of 0.01?

What approximations r going to help? I can not do with Riemann,Trapezoidal and Simpson.
 
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WayneH said:
Q: How many terms of the alternating series \sum((-2)^n)/n! needed to find the sum to an accuray of 0.01?

What approximations r going to help? I can not do with Riemann,Trapezoidal and Simpson.
This is not a precalculus question. You should post problems like this in the Calculus & Beyond section.

Your text should provide information about error estimates for alternating series, namely that the first unused term in the series gives a bound for the error.
 

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