So at first glance it appeared pretty easy, we can assume by contradiction that sn converges to some constant L, then $\lim(\frac{S\_n}{n})$ as n approaches infinity is $\lim(\frac{L}{n})$ which is zero hence a contradiction (0>0 wrong statement). but after thinking about it $\lim(\frac{L}{n})$ approaches zero but never exactly zero,so the statement $\lim(\frac{L}{n})>0$ is not wrong. am i overthinking this?