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Homework Help: Converging series

  1. Dec 10, 2008 #1
    hi :)
    Quick questions:

    How can I write a series converging into the limit of pai ?

    Prove that the limit of the series zz (n+2) / (2n² +1) zz is not 1/2 when n->infinity (and bigger than 1)


    I came to the equation:
    zz |(-2n² + 2n +3) / (2n² +1) | >= ε zz

    (*)And I made the left expression smaller by enlarging the denominator and diminution the numerator:

    zz |(-2n² + 2n) / (2n² +n) | >= ε zz
    which is
    zz |(-2n + 2) / (2n +1) | >= ε zz
    and again.. (*)
    zz |(-2n) / (2n +n) | >= ε zz
    which is
    zz |-2/3 | >= ε zz

    and then I can choose ε = 2/3 ?
    something dosent seem right ..
     
  2. jcsd
  3. Dec 10, 2008 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Are those "zz"s suppose to delimit mathematical expressions? Please don't do that- especially not without explanation!

    The simplest thing to do is to divide both numerator and denominator by n2 so that you get ((1/n)+ (2/n2))/(2+ (1/n)). Now you should be able to see that, as n goes to infinity, those fractions go to 0.


     
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