c With y n and w n as above we have that by definition of supremum and infimum

# C with y n and w n as above we have that by

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c)Withynandwnas above we have that, by definition of supremum and infimumwnanynfor allnNand sownynfor allnN. By the Order Limit Problem 4.2:(Abbott 2.4.1)a)Prove that the sequence defined byx1= 3 andxn+1=14-xnconverges.b)Now that we know limxnexists, explain why limxn+1must also exist and equalthe same value.c)Take the limit of each side of the recursive equation in part (a) to explicitlycompute limxn. 2
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• Spring '15
• AmarjitNijjar
• Mathematical analysis, Limit of a function, Supremum, Limit of a sequence, Limit superior and limit inferior, Dominated convergence theorem