Work these on notebook paper. Use your calculator on problems 1 - 5, and give decimal answers correct to three decimal places. 1. Approximate the sum, S, of the series (-1)" n! n=0 by using its first five terms, and explain why your estimate differs from the actual value by less than .009. Then use your results to find an interval in which S must lie. 2. Approximate the sum, S, of the series 00 (-1)"+13 2 by using its first six terms. Use the alternating n=1 n series error bound to show that this approximation differs from the actual value by less than .07. Then use your results to find an interval in which S must lie. 3. Approximate the sum of the convergent series (-)" n=0 2"n! so that the error will be less than 1000 1 1000 How many terms were needed? What are the properties of the terms of this series that guarantee that your approximation is within of the exact value? Justify your answer. 8 4. Approximate the sum of the convergent series n=0 (-1)" (2n)! 1 so that the error will be less than 1000 1 1000 How many terms were needed? What are the properties of the terms of this series that guarantee that your approximation is within of the exact value? Justify your answer. 5. Approximate the sum of the convergent series ** (-1) "+1 1 3 so that the error will be less than n n=1 1200 How many terms were needed? What are the properties of the terms of this series that guarantee that 1 your approximation is within of the exact value? Justify your answer. 1200