Given the series (-1)^n.tan(1/n) how do I study its nature in terms of divergence and convergence?

Question

I have a series whose general term is tan(1/n)*(-1)^n and I want know if it is divergent or convergent, how do I proceed?

I have tried stablishing upper and lower limits and the ratio test and all I indicated that it was divergent.Turns out, it is not.Can you help me?

Answer 1

Hint: Apply the alternating series test.