Convergent Series: Find Sequence of Positive Reals

[rainwyz0706]

Homework Statement

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.

Homework Equations

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!

 

[Dick]

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