The Degree Isn't Given Either?

Algebra Level 5

Let $a_1, a_2, \ldots , a_n$ be the roots of the equation $\displaystyle \sum_{k=1}^n kx^k = 0$ . If $\displaystyle \sum_{k=1}^n \dfrac1{1-a_k} = 7$ , find $n$ .