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Consider the convergent alternating series (-1)^n. Let Sn be the nth partial sum of this series. Compute Sn and Sn 1 and use these values to find bounds on the sum of the series. If n = 4, then Sn and Sn 1 are -1 and 0 respectively. Therefore, the sum of the series lies within the interval [-1, 0]. This interval estimate for the value of the series has an error of |Sn - (-1)|.

Consider the convergent alternating series (-1)^n. Let Sn be the nth pa…

2022年6月2日

SOLVED: Let Sn be the nth partial sum of a series. In the following exercises, a convergent alternating series is given, and a value of n. Compute Sn and Sn 1 and use these values to find bounds on the sum of the series:(-1)^n 21. n = 5 n= In(n 1) SolutionS5 = -1.1906; S6 = -0.6767; (-1)^2 -1.1906 < 0.6767 In(n 1)(-1)^(n 1) 22. n = 4 n^4 n Solution

SOLVED: Let Sn be the nth partial sum of a series. In the following e…

2021年10月20日

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Given a positive integer n written in decimal form, the alternating sum of the digits of n is obtained by starting with the right-most digit, subtracting the digit immediately to its left, adding the next digit to the left, subtracting the next digit, and so forth. For example, the alternating sum of the digits of 180,928 is 8-2+9-0+8-1=22. Justify the fact that for any nonnegative integer n, if the alternating sum of the digits of n is divisible by 11 , then n is divisible by 11 . | Numerade

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