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Limit and Convergence

  1. Nov 6, 2013 #1
    Suppose a_n > 0 and b_n > 0 for all n in natural number (N). Also, lim a_n/b_n = 0 as n goes to infinity. Then the sum of a_n converges if and only if the sum of b_n converges ...both from 1 to infinity.

    My approach is that lim a_n/b_n = 0 means that there exists N in natural number (N) for which |a_n/b_n - 0| < 0 for all n >= N. Then 0 < a_n < 0. The sum of a_n from 1 to infinity is 0. So The sum of a_n from 1 to infinity is convergent.

    Is this proof that easy or I miss something?
     
  2. jcsd
  3. Nov 6, 2013 #2

    tiny-tim

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    Hi Askhwhelp! :smile:
    "if and only if"? … that obviously isn't true

    do you mean "if", or do you mean lim a_n/b_n = 1 ? :confused:
    sorry, but that doesn't even make sense :redface:

    check the wording of the question, and start again :smile:
     
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