I know that if the series of (a)n (n is a subscript) converges, then the lim (a)n=0. How can I show that if the series of (a)n converges, then lim n(a)n=0? Or rather if a1 +a2 +a3 +...+an=0, then lim n*(a)n=0? Not sure how to show this, but I know the proof involves the cauchy criterion for series. Help anyone?