Show that if ∑a_n converges, then ∑ from N to ∞ of a_n -> 0 as N goes to ∞.

My first thought was to basically let a_n = s_n - s_(n-1). And since a_n and s_n are both convergent, just take the limits of s_n and s_(n-1) as n -> ∞ and show they both equal zero.