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Prove the absolute convergence test:
Let the sum from n=m to infinity of a_n be a formal series of real numbers. If this series is absolutely convergent, then it is also conditionally convergent. Furthermore, in this case we have the triangle inequality - the absolute value of the sum from n=m to infinity of a_n <= the sum from n=m to infinity of the absolute value of a_n.
Use the following propositions to justify your answer:
Let the sum from n=m to infinity of a_n be a formal series of real numbers. Then the sum from n=m to infinity of a_n converges if and only if, for every real number epsilon>0, there exists an integer N<=m such that the absolute value of the sum from n=p to q of a_n <= epsilon for all p, q>= N.
and
Triangle inequality for finite series: let m<=n be integers, and let a_i be a real number assigned to each integer m<= i <= n. Then we havethe absolute value of the sum from i=m to n of a_i <= the sum from i=m to n of the absolute value of a_i.
Write the generator matrix. Show by example that your code will detect 1 error, 2 errors, and 3 errors. Give an example where 4 errors are made in transmitting a message word, but your code does not detect any errors.
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A recent article suggested that if you earn $25,000 a year today and the inflation rate continues at 3 percent per year, you'll need to make $33,598 in 10 years to have the same buying power.
Please show how to solve each of the following problems. Find the antiderivative (integral)
Suppose you randomly draw two marbles, without replacement from a bag, containing six green, four red and three black marbles. a) Determine the probability that both marbles are red.
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Probability Mass Function, Mean and Variance A lot consisting of 100 fuses is inspected by the following procedure: 5 fuses are selected randomly, and if all 5 "blow" at the specified amperage
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Calculating Production and Material Consumption Rates, The Ottawa Coat company manufactures winter coats and spring jackets. The winter coat requires 4m of material while the spring jacket requires just 1m
Let f: [a,b] ----> R and suppose f is integrable with respect to alpha. Prove that for any c in the real numbers, cf is integrable with respect to alpha and the integral from a to b of cf d(alpha) = c times integral from a to b of f d(alpha).
A body at temperature of 55 degree F is placed outdoors where the temperature is 110 degree F. After 5 minutes the temperature of the body is 65 degree F.
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