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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.
I want to prove that a population mean is not 150. Use an alpha of 5 percent & set up the full, detailed, five step hypothesis test. Suppose when the sample 200 is taken the sample standard deviation is ten & the sample mean is 151.77.
How many different passwords can be formed? b) How many different passwords have no repeated number or letters?
This solution provides an analysis of how we evaluate personality theory over time, and how and why historical personality theories lend themselves to understanding people and events in modern times.
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The marginal revenue for a certain product is given by dR/dx = 25-2x. Find the change in revenue when sales increase from 7 to 10 units.
Find the hypothesis
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Hypothesis test for two differences between means
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If f is an automorphism of S_3, prove that there exists a sigma in S_3 such that f(tau)
Find the general solution for given trigonometric equation on the given interval.
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