Sustainability of Collusion in a finite Bertrand competition with N > 2 firms
You're already on the right track. Just need to reorganize your argument a little bit.
Hint: Prove by contradiction. Suppose that collusion is sustainable in an equilibrium. Show that the collusive strategy (i.e. choosing the monopoly price in every stage) is not optimal given that everybody else is doing the same. Then conclude that collusion cannot be an equilibrium, hence a contradiction.