Question: Calculating a sum and subsequently taking the limit

I have this sum which should be equal to argument(GAMMA(I*x)) with x>0.


`assuming`([x*ln(n)-(1/2)*Pi-(sum(arctan(x/k), k = 1 .. n))], [x > 1]);

aG := `assuming`([limit(%, n = infinity)], [x > 1]);

`~`[evalf](eval([aG, argument(GAMMA(I*x))], x = 1))


However this limit evaluation is somehow broken in as it always gives some order symbol O(1) etc..

What is happening here?

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