The problem is:
For infinite independent Bernoulli trials, prove that the total number of successful trials $N$ have the following property:
$ [N < \infty] = \bigcup\limits_{n=1}^{\infty}\,[N \le n] $
Actually this is just part of bigger problem in a book, and the equation is given as an obvious fact and as a hint without any explanation. What does the equation exactly mean? I guess square brace means set, but what's the definition of $[N < \infty]$?