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December 6th, 2010, 12:26 PM  #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 bnB<E. Let M=[(B)/2]. thus for n?N, bn=bnB+B?BbnB?B[(B)/2]=[(B)/2]=M what variations do i need to make in the proof for the lemma? 
December 6th, 2010, 01:46 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, 01:58 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, 02:35 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 such that , where are intiger and real from lemma. The remaining sequence elements modules are of course greater then [latex]M>M'[latex].


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convergenceplease, proof 
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