Calculate $ lim_ {x to infty} $ $ e ^ {- x} sum_ {k = 0} ^ {[x]} frac {x ^ k} {k!} = frac {1} {2} $

How to prove:$ lim_ {x to infty} $ $ e ^ {- x} sum_ {k = 0} ^ {[x]} frac {x ^ k} {k!} = frac {1} {2} $. Thanks in advance.