Generalized Binomial Expansion

Probability Level 3

If the function $f(x) = \sqrt{1 + x}$ is expanded out in terms of powers of $x$ such that $f(x) = \sum\limits_{k=0}^{\infty} a_{k} x^{k},$ what's the coefficient $a_{3}$ of the $x^{3}$ term?

Express your answer as an exact decimal.