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Assignment -
Use the remainder rule for alternating series to approximate the sum of the series n=1Σ∞(-1)n+1/2n with an error of less than 0.005 by following the steps below.
1. Find the smallest number of terms, N, that you must use to produce an approximation that has an error of less than 0.005. To do this, calculate the absolute values of the terms of the series using different values of n, until you reach the smallest n for which the absolute value of the term is less than 0.005.
2. Once you have found N, find the partial sum, SN, of the first N terms of the series. Express your answer as a decimal number accurate to 3 decimal places.
Verified Expert
We used the Remainder Estimation of alternating series to approximating the Infinite Alternating series. In this problem, the series is converges, that's why, we calculated. And also it gives us a process to approximate the sum of alternating series with a remainder. Here, the given series is decreasing, that's why we used this theorem to calculate the Approximation. The Solution has been prepared in Microsoft office word document.
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