Sum n=1 to infinity of sin(1/n^2)

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Sum n=1 to infinity of sin(1/n^2)
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i have a question. Can you help me with the following series please?
series from n = 1 to infinity of ( (-1) ^ (n-1) * n * sin ( 1 / (n^2) ) ). This diverges of converges? I tried with Leibniz but the limit gets infinity so it is different of 0. I tried with absolute convergence but i get that the absolute series diverges so the alternating series is not absolutely convergence. Help me out please..

AlexandruDiaconu-yl