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 :

(5n^4)+1/((150,348n^3)+999)

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.

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