A set C is convex if the line segment between any two points in C lies in C, i.e., if for any x1,x2C and any with 01, we have x1+(1)x2C Problem A [5 points]: Let CRn be a convex set, with x1,,xkC, and let ,,kR satisfy i0, and 1++k=1. Show that 1x1++kxkC. Hint: The definition of convexity is that this holds for k=2; you must show it for arbitrary k