$ \lim\limits_{n\rightarrow \infty} {\frac{B_{t}}{t}}$ Brownian Motion

Question

I want to prove in two ways that $ \lim\limits_{n\rightarrow \infty} {\frac{B_{t}}{t}}\rightarrow 0$ almost surely, where $B_{t}$ is a standard Brownian Motion.

1) in $L^2$

Can we say $X_{t}={\frac{B(t)}{t}}$ and compute that the $E[(X_{t_{i+1}}-X_{t_{i}})^2] \rightarrow0$, as $t\rightarrow \infty$ ?

2) in almost surely convergence limit

I want to prove in #2 using the properties that:

a. $ \lim\limits_{t\rightarrow \infty} X_{t}(w)=X(w)$ almost surely

b. $P(w|X_{t}(w) - X(w))=1$

Please help.. Any help will be appreciated...