Let $(B_t)_{t \geq 0}$ is a Brownian motion and $\{ t_n \}_{n \geq 1}, \forall n\ t_n \geq 0$ a sequence of numbers such that $\sum_{n=1}^{\infty} t_n^{-1/2} < \infty $. Proof, that $| B_{t_n} | \underset{n \to \infty}{\to} \infty$ a.s.
I don't have any good idea how to solve this.