Let A = {image} and B = {image} . Compare A and B.

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Presentation transcript:

Let A = {image} and B = {image} . Compare A and B. A > B A < B A {image} B A = B 1. 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

the series is convergent the series is divergent Use the Integral Test to determine whether the series is convergent or divergent. {image} the series is convergent the series is divergent 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Series A is divergent, series B is convergent. Given the two series {image} and {image} . determine whether each series is convergent or divergent and choose the correct statement. Series A is divergent, series B is convergent. Series A is convergent, series B is divergent. Both series are convergent. Both series are divergent. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

{image} 0.5 {image} 0.500001 {image} 0.499999 {image} 2.3 1. 2. 3. 4. Use the sum of the first 10 terms to estimate the sum of the series {image} . Estimate the error in using {image} as an approximation to the sum of the series (use the comparison by the integral {image} ). {image} 0.5 {image} 0.500001 {image} 0.499999 {image} 2.3 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

m > {image} m < {image} 1. 2. 3. How many terms of the series {image} would you need to add to find its sum to within 0.5? m > {image} m < {image} 1. 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50