Okay, I understand the issue now, I think. So, summing up the effect of all the future rounds in exactly the way you are describing is something you would do to determine if grim trigger is an equilibrium strategy. (If you defect now, you get punished in ALL future rounds) However, in tit for tat, your punishment for defecting only lasts for 1 round, so you don’t have to add all that up.
Okay, I understand the issue now, I think. So, summing up the effect of all the future rounds in exactly the way you are describing is something you would do to determine if grim trigger is an equilibrium strategy. (If you defect now, you get punished in ALL future rounds) However, in tit for tat, your punishment for defecting only lasts for 1 round, so you don’t have to add all that up.