We have given a series,

\(\sum_{n=1}^\infty(-1)^n\sin^2n\)

We know that for the alternating series test, series should be given in forms,

\(\sum_{n=1}^\infty(-1)^na_n\quad\text{or}\quad\sum_{n=1}^\infty(-1)^{n+1}a_n\)

Our series is given in the form,

\(\sum_{n=1}^\infty(-1)^na_n\)

Conditions for alternate series are, \(a_n>0\)

And

\(\lim_{n=\infty}a_n=0\)

And series should be in decreasing order to be a series convergent.

\(\lim_{n=\infty}\sin^2n\cdot n\ne0\)

Hence, the given series is not convergent.

\(\sum_{n=1}^\infty(-1)^n\sin^2n\)

We know that for the alternating series test, series should be given in forms,

\(\sum_{n=1}^\infty(-1)^na_n\quad\text{or}\quad\sum_{n=1}^\infty(-1)^{n+1}a_n\)

Our series is given in the form,

\(\sum_{n=1}^\infty(-1)^na_n\)

Conditions for alternate series are, \(a_n>0\)

And

\(\lim_{n=\infty}a_n=0\)

And series should be in decreasing order to be a series convergent.

\(\lim_{n=\infty}\sin^2n\cdot n\ne0\)

Hence, the given series is not convergent.