Define thedistancebetween two vectorsuandvin $\displaystyle R^n$ as d(u,v) = ||u-v||Show that d(u,w) <= d(u,v) + d(v,w)

My work:

$\displaystyle ||u-v|| + ||v+w||=\sqrt{(u_1-v_1)^2+(u_2-v_2)^2+...+(u_n-v_n)^2}+\sqrt{(v_1-w_1)^2+(v_2-w_2)^2+...+(u_n-w_n)^2}$