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 December 6th, 2010, 11:26 AM #1 Newbie   Joined: Dec 2010 Posts: 4 Thanks: 0 proof of convergence....please help! Problem: Prove if {bn} converges to B and B ? 0 and bn ? 0 for all n, then there is M>0 such that |bn|?M for for all n. What I have so far: I know that if {bn} converges to B and B ? 0 then their is a positive real number M and a positive integer N such that if n?N, then |bn|?M . (by lemma) PROOF (of lemma)- since B ? 0, (|B|)/2=E>0. There is N such that if n?N, then |bn-B|
 December 6th, 2010, 12:46 PM #2 Senior Member   Joined: Nov 2010 Posts: 502 Thanks: 0 Re: proof of convergence....please help! That's pretty much the right idea.
 December 6th, 2010, 12:58 PM #3 Newbie   Joined: Dec 2010 Posts: 4 Thanks: 0 Re: proof of convergence....please help! i know that it is similar but there are some differences......im just not sure what they are
 December 6th, 2010, 01:35 PM #4 Newbie   Joined: Dec 2010 Posts: 7 Thanks: 0 Re: proof of convergence....please help! The only diffrence is a general quantifier placed in proposed problem. After proving this lemma it is almost done- consider $M'$ such that $0, where $n,M$ are intiger and real from lemma. The remaining sequence elements modules are of course greater then [latex]M>M'[latex].

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