i'm having difficulty proving the following:

let p_i(i in naturals) be a sequence of pts in R^n and p_0 be a point in R^n. let p_i=(p_i,1 , ... , p_i,n) for i in naturals and p_0 = (p_0,1 , ... , p_0,n). show that lim(i goes to infinite) p_i = p_0 if and only if lim(i goes to infinite) p_i,k = p_0,k for every k=1,...,n.