`a_n = nsin(1/n)` Determine the convergence or divergence of the sequence with the given n'th term. If the sequence converges, find its limit.

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Apply n'th term test for divergence, which states that, 

If `lim_(n->oo) a_n!=0` , then `sum_(n=1)^ooa_n` diverges


Apply L'Hospital's rule,

Test L'Hospital condition:`0/0`






By the limit chain rule,



So, by the divergence test criteria series diverges.  

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