1. May 19, 2009 #1

   asset101

   

   let an = [tex]\frac{(2n+1)}{(3n+7)}[/tex]. Prove direct from definition that an[tex]\rightarrow2/3[/tex].
   
   Any help would be appreciated.
   Cheers

    

   asset101, May 19, 2009
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3. May 19, 2009 #2

   tiny-tim

   

   Science Advisor

   Homework Helper

   ok … first step in a question like this is …
   
   

   what is the definition of the statement "lim((2n+ 1)/(3n+7)) = 2/3"? ​

    

   tiny-tim, May 19, 2009
4. May 19, 2009 #3

   AUMathTutor

   

   Here's an idea... as long as n isn't zero, the following two things are the same:
   
   (2n+1)/(3n+7) = [(2n)(1+1/2n)]/[(3n)(1+7/3n)]
   
   What happens as the n's get bigger and bigger to the terms 1/2n and 7/3n?

    

   AUMathTutor, May 19, 2009
5. May 19, 2009 #4

   HallsofIvy

   

   Staff Emeritus

   Science Advisor

   That's the simplest way of finding the limit but it doesn't "prove from the definition".

    

   HallsofIvy, May 19, 2009

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