To achieve an accuracy of 0.01 in the alternating series \(\sum \frac{(-2)^n}{n!}\), it is essential to consider the error estimates for alternating series. The error can be bounded by the first unused term in the series, which means that if the absolute value of this term is less than 0.01, the approximation is sufficiently accurate. For this series, calculating terms until the factorial in the denominator results in a term smaller than 0.01 is necessary to determine the required number of terms.
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This is not a precalculus question. You should post problems like this in the Calculus & Beyond section.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.