1. The problem statement, all variables and given/known data Show that |x_1 + x_2 + · · · + x_n | ≤ |x_1 | + |x_2 | + · · · + |x_n | for any numbers x_1 , x_2 , . . . , x_n 2. Relevant equations |x_1 + x_2| ≤ |x_1| + |x_2| (Triangle inequality) 3. The attempt at a solution I tried using the principle of induction here, but to no avail. Can I induct on the basis |x_1| ≤ |x_1| ?