Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Prove direct from definition

  1. May 19, 2009 #1

    asset101

    User Avatar

    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
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. May 19, 2009 #2

    tiny-tim

    User Avatar
    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"? :smile:​
     
    tiny-tim, May 19, 2009
  4. May 19, 2009 #3

    AUMathTutor

    User Avatar

    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

    User Avatar
    Science Advisor

    That's the simplest way of finding the limit but it doesn't "prove from the definition".
     
    HallsofIvy, May 19, 2009
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook