Question

determine the nature of the series​

Answer 1

Answer:

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!