Expected value and variance of random walk sum Sn

[erica1451]

Homework Statement

Let (X1, X2, ..., Xn,...) be iid increments (with mean µ and variance ∂^2) of a random walk Sn=X1+X2+...+Xn. What are the expected value, variance of Sn?
Prove that lim n-> ∞ Sn =+ ∞ if µ>0 and lim n-> ∞ Sn =- ∞ if µ<0

Homework Equations

The Attempt at a Solution

I found that E(Sn)=nµ and Var(Sn)=n∂^2. I am not sure how to do the second part though.

 

[EnumaElish]

What is the definition of lim Sn?