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!