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Math 104: Homework 3-
1. Let (an) be a sequence defined according to a1 = t where t > 0, and an+1 = 2an/(1+an) for n ∈ N. Prove that an → 1 as n → ∞.
2. Let (sn) and (tn) be Cauchy sequences defined on R, and let (un) be a sequence defined as un = asn + btn for all n, where a, b ∈ R. By using the definition of a Cauchy sequence only, without assuming that limits of (sn) and (tn) exist, prove that (un) is a Cauchy sequence.
3. Let (sn) be a sequence defined for n ∈ N as
Calculate the monotonic sequences
uN = inf{sn : n > N}, vN = sup{sn : n > N}
for each N ∈ N and hence determine lim inf sn and lim sup sn.
What is the probability that a random sample of n = 242 people from the general population will have a mean IQ score that is less than or equal to 87?
Multiple choice question from Probability and Set Language and valid probability distribution for a sample space
n-state tuition and fees at Virginia Commonwealth University (VCU) was $9517 for the 2011-12 academic year. The CPI for 2011 was 224.9 and the CPI for 2001 was 177.1. What is the 2011-2012 tuition in 2001 dollars
Stating the null & alternate hypotheses
How many numbers must be selected from the set A = {1, 3, 5, 7, 9, 11, 13, 15} to guarantee that at least one pair of these numbers add up to 16? Explain and justify your answer.
The objective is to minimize the sum of the completion times of all the jobs. Provide an integer programming formulation for this problem.
use the precise definition of a limit lim x --gt infinity of fxl to prove that lim x --gt infinity of xcosxx
A grain silo has a cylindrical shape. Its diameter is , and its height is . What is the volume of grain that can be stored in the silo?
Locate your local Chamber of Commerce's community profile either online or in printed material that describes your local community. Write a three to four (3-4) page paper on the following:
Find the equation of the regression line. Graph the line . Determine the slope and y-intercept of the regression line.
An item is sold under H.P on a deposit of Ksh 600 and 12 monthly instalments of Ksh 300 each.If the H.Pprice is 12% higher than the cash price, what is the cash price?
How much should they invest in each type of bond to maximize income if the amount in the stable bond should not exceed the amount in the more volatile bond? What is the maximum income?
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