Homework 4 Solution - Real Analysis Problem Set 4 Solutions Drew D Ash pg 49 Exercise 2.3.7 part a Let(an be a bounded(not necessarily convergent

# Homework 4 Solution - Real Analysis Problem Set 4 Solutions...

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Real Analysis Problem Set 4 Solutions Drew D. Ash April 30, 2013 pg. 49 Exercise2.3.7parta:Let(an)be a bounded (not necessarily convergent) sequence, and assumelimbn= 0. Show thatlim(anbn) = 0. Why are we not allowed to use the Algebraic Limit Theorem to provethis? pg. 54 Exercise 2 . 4.2:(a)Prove that the sequence defined byx1= 3andxn+1=14-xnconverges.(b)Now that we knowlimxnexists, explain whylimxn+1must also exists and equal the same value.(c)Take the limit of each side of the recursive equation in part(a)of this exercise to explicitly computelimxn. 1

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• Fall '11
• JimHagler
• Algebra, lim, Mathematical analysis, Limit of a sequence, Xn, Dominated convergence theorem