17: The cosine contributes signs ...+ 0 − 0 + 0 − 0 +... to the terms of the series, so this series is not alternating. However, note that when we discard the terms that are zero anyway, we get a series whose signs do alternate. In order to get a good handle on this we rewrite the series using the fact that terms are non-zero exactly when k is even, it takes a little experimentation to get the signs right. In fact,
If you did not enjoy playing with the signs and rewriting, there was a possibility to go right to absolute convergence and hope that it comes out positive.