Q: Suppose that {Xn} converges to X. For each n within the set of Natural Numbers, define Yn = (X1+X2+...+Xn)/n. Prove that {Yn} also converges to x.

My solution: So far, I can only think of this as a continuous function problem. I set {Yn} as a function of Y(x). So if Y(x) is continuous, then Y(Xn) -> Y(x).

Am I having the right idea?

Thank you.

KK