is it converges absolutly ,or conditionally convergent

or is it diverges?

$\displaystyle \sum_{k=1}^{infinity}(-1)^{k}sin\frac{1}{k}$

the absolute value series is |sin(1/k)|<=|1/k|

which is diverges

but it gives me nothing

because if it where convergent then the smaller one would converge

but here the bigger one diverges(harmonic series)

??