On a line, there are particles located at 1, 2, 3, 4, and 5. Their masses are 1, 2, 3, 4, and 5, respectively.
(a) What is the center of mass of the system?
(b) If we add a particle of mass 6 at 6, what is the center of mass?
(c) If we add particles of mass j at j for j = 6 to n, what is the center of mass? Power sums that were introduced in Section 5.1 will be helpful here.