Answer
$$\sum_{k=1}^{5} (-1)^{k+1}(k^3-1)$$
Work Step by Step
The sequence involves a sum with alternating signs (positive, then negative, then positive, and so on...).
This means that the summation involves either $(-1)^k$ or $(-1)^{k+1}$.
The first term is positive so $(-1)^{k+1}$ will be used.
The terms of the summation is of the form $(k^3-1)$ where $k$ is a counting number starting with $1$.
The summation has 5 terms so $k$ is from 1 to 5 only.
Thus, the summation notation whose expanded form is given is:
$$\sum_{k=1}^{5} (-1)^{k+1}(k^3-1)$$