SEE THIS As you see [imath]\mathop {\lim }\limits_{n \to \infty } \left( {1 - \cos \left( {\frac{{n - 1}}{{{n^2}}}} \right)} \right) = 0 [/imath] it passes the first test, so it may converge. i.e. it is not necessarily divergent.
This is a complicated argument: SEE HERE
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