determine the nature of the series
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Consider the following series :
∑n=1∞sin(n)cos(1n)n+2−−−−−√∑n=1∞sin(n)cos(1n)n+2
We want to determine if the series diverges or not.
I tried so far using the small-angle approximation for the cosine, but it turned even messier. Is this problem as tough as I see it, or is it there something obvious that I'm overlooking ? If anyone gets any ideas towards a solution I would be most welcome!
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