Convergent series and their corresponding sequences (analysis course)

[v.rad]

If a_n >= 0 for all n, and the series a_n converges, then n(a_n - a_n-1) --> 0 as n --> infinity.

Prove or disprove the statement using a counterexample.

I know that the statement is false...I am just having terrible difficultly finding a counterexample...

 

[mynameisfunk]

actually... http://www.mathhelpforum.com/math-help/f57/limit-question-indeterminate-forms-159597.html