1. The problem statement, all variables and given/known data Use the triangle inequality to prove that [itex] \left| s_n - s \right| < 1 \implies \left| s_n \right| < \left| s \right| +1[/itex] 2. Relevant equations The triangle inequality states that [itex]\left| a-b \right| \leq \left| a-c \right| + \left| c-b \right|[/itex] 3. The attempt at a solution So far I have [itex] \left| s_n - s \right| < 1 \implies -1 < s_n - s < 1 \implies s_n < s + 1[/itex]. But now I don't see how I can use the triangle inequality to move forward. Hints greatly appreciated, no spoilers please!