$\displaystyle \sum(-1)^{n}[1-nsin(1/n)]$ determine if A.convergent, C.convergent or divergent

I chose C.Convergent

I saw that nsin(1/n) goes to 1 because of some other question I solved earlier and that would make everything 0

which means that $\displaystyle a_k \rightarrow 0$ making the series conditionally convergent?

if this is wrong, could you please point out what my error of thinking about this is? from what you see how I analyzed this atleast...

thanks