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How did this come up?
Trigonimetric function in the denominator, evaluated at non-integer points, is very difficult to handly.
I'd naively assume the ints hit sin too hard, givin small sin(n), making the thing diverge even though it's supressed by 1/n^3. But it's hard to say for such tough ones.
Mathematica doesn't know either, I think.
Search StackExchange for similar problems - I know they have some.
