Sum is_convergent gives incorrect result

[proy87]

Sum(1-cos(1/x), (x,1,oo)).is_convergent() gives False, but this series is convergent.

[oscargus]

The reason seems to be that the order of the expression is O(1, (_x, oo)), and, hence, the p_series_test (x**p) returns p = 0 and hence it is deemed to not be convergent. So more or less does SymPy think that the function behaves as a constant near oo and hence is not convergent.

So the O method should be changed to return something else.

[anutosh491]

Well this is error is a really good catch , as we can't comment much on sum of two divergent series . But O(1-cos(1/x) , (_x, oo)) gives O(1, (_x, oo)) which doesn't seem wrong and may be the preferred test for this series would be the integral or any of the comparision tests. Not sure if we can go by the p_series_test here as not all methods can be used for a particular series !!!