statistical mechanics - Is ${e^{ikx}} to {x^2}$ when $k to 0$

in an online video lecture,(around 36min, where the exactly statement is at 36min33secs.) i got one question, suppose we have a system of $N$ particles, $\left\{ {{{\vec r}_i}(t)} \right\}i = 1, \cdot \cdot \cdot ,N$ are the position vectors of the particles. I was told in the lecture that the so-called self intermediate scattering function is defined as.

$${F_s}(k,t) = \frac{1}{N}\left\langle {\sum\limits_{i = 1}^N {{e^{i\vec k \cdot [{{\vec r}_i}(t) - {{\vec r}_i}(0)]}}} } \right\rangle.$$ (for homogeneous system, it only depends on the absolute value of $\vec k$.)

Furthrmore, it is said by the lecturer that when $k \to 0$,

$${F_s}(k,t) \to \frac{1}{N}\left\langle {\sum\limits_{i = 1}^N {{{[{{\vec r}_i}(t) - {{\vec r}_i}(0)]}^2}} } \right\rangle$$

but i can't see why. Could anybody give me some help on it.