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13 Nov 2019
EXAMPLE 5 (a) Approximate the sum of the series Σ 1/ng by using the first 10 terms. Estimate the error involved in this approximation. (b) How many terms are required to ensure that the sum is accurate to within 0.0005? SOLUTION In both parts (a) and (b) we need to knowf(x) dx. With f(x)-1/x, which satisfies the conditions of the Integral Test, we have 8n (a) Approximating the sum of the serles by the tenth partial sum, we have 19 2 39 10 1.0020 rounded to four decimal places) According to the remainder estimate in the Remainder Estimate for the Integral Test, we have 10 x so the size of the error is at most 0.00000000125 (b) Accuracy to within 0.0005 means that we have to find a value of n such that Rn s 0.0005. Since we want 250 We need terms to ensure accuracy to within 0.0005
EXAMPLE 5 (a) Approximate the sum of the series Σ 1/ng by using the first 10 terms. Estimate the error involved in this approximation. (b) How many terms are required to ensure that the sum is accurate to within 0.0005? SOLUTION In both parts (a) and (b) we need to knowf(x) dx. With f(x)-1/x, which satisfies the conditions of the Integral Test, we have 8n (a) Approximating the sum of the serles by the tenth partial sum, we have 19 2 39 10 1.0020 rounded to four decimal places) According to the remainder estimate in the Remainder Estimate for the Integral Test, we have 10 x so the size of the error is at most 0.00000000125 (b) Accuracy to within 0.0005 means that we have to find a value of n such that Rn s 0.0005. Since we want 250 We need terms to ensure accuracy to within 0.0005
Trinidad TremblayLv2
7 Jul 2019