Prove direct from definition

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  • #1
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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
 

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  • #2
tiny-tim
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ok … first step in a question like this is …

what is the definition of the statement "lim((2n+ 1)/(3n+7)) = 2/3"? :smile:
 
  • #3
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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?
 
  • #4
HallsofIvy
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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?
That's the simplest way of finding the limit but it doesn't "prove from the definition".
 

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