1. The problem statement, all variables and given/known data I understand everything except the last two lines. I am really confused about the last two lines of the proof. (actually I was never able to fully understand it since my first year calculus) I agree that if ALL three of the conditions n≥N, k≥K, and nk≥N are satisfied, then the last line is true. But why does the condition n≥N alone imply that the last line is true? Does n≥N guarantee that k≥K, and nk≥N? Why is it true that n≥N => |an-an_k| < ε/2 ? And why is it true that n≥N => |an_k-L| < ε/2 ? Can somebody kindly explain the last two lines of the proof in more detail? 2. Relevant equations N/A 3. The attempt at a solution N/A Any help is much appreciated!