In math we describe a function Converge or Diverge based on its ending behavior as x approches positive or negative infinity.
If a fuctions approches inf. as x approches positive or negative infinity, then the function is diverge.
On the other hand, If a function approaches a certain value as x apporaches positive or negative inf, then the function is Converge.
In your example :
as n approaches inf., the function approches 0 , so the function is converge to 0.
and the series:
2,1, 2/3, 1/2, 2/5,....
the series is clearly approching 0 as n values approaches inf. then the series is Converge to 0.