Math Is Fun Forum

Eigma

Member

Registered: 2009-02-22

Posts: 5

proving approximation and series

Hi. I came across your site while surfing the net. I think this is great... but I posted my first problem in the wrong place maybe due to excitement. Sorry . To start again, I'm really confused how to begin proving sequences. Can you give me a technique, for example, how to prove that if an-->A and bn-->B, then an/bn --> A/B where bn and B is not 0?

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"A smile is a curve that can set things straight."

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: proving approximation and series

Have you done any proofs with epsilons before?  (You'll know what I mean if you have)

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: proving approximation and series

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: proving approximation and series

Have a look at this thread: http://www.mathisfunforum.com/viewtopic.php?id=11477

Ignore the abstract-algebra stuff and anything else not relevant to you, and just concentrate on the results about sequences. I considered sequences of rational numbers only, but the results should also work for sequences of real numbers. I also used Cauchy convergence rather than convergence to a limit – for real numbers, however, those two types of convergence are equivalent.

Eigma

Member

Registered: 2009-02-22

Posts: 5

Re: proving approximation and series

Thanks for the advise ma'am.

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"A smile is a curve that can set things straight."