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Convergent series

  1. May 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Find a sequence (an) of positive real numbers such the sum of an from 1 to infinity is convergent but the number of k such that a(k+1)>ak divided by n tends to 1 as n tends to infinity.

    2. Relevant equations

    3. The attempt at a solution
    I don't have a clue how to find a sequence here. Could anyone please give a hint? Any help is appreciated!
  2. jcsd
  3. May 24, 2010 #2


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    Homework Helper

    Be creative. Take a nice convergent decreasing series like 1/2^n. Now think about ways of rearranging the terms.
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