with the sum running over all possible values of n enumerating the standing waves. The factor of ⁠ 1 / 2 ⁠ is present because the zero-point energy of the n th mode is ⁠ 1 / 2 ⁠ E n, where E n is the energy increment for the n th mode. (It is the same ⁠ 1 / 2 ⁠ as appears in the equation E = ⁠ 1 / 2 ⁠ ħω.) Written in this way, this sum is clearly divergent; however, it can be used to create finite expressions.