The Degree Isn't Given Either?

Algebra Level 5

Let a1,a2,,ana_1, a_2, \ldots , a_n be the roots of the equation k=1nkxk=0\displaystyle \sum_{k=1}^n kx^k = 0 . If k=1n11ak=7 \displaystyle \sum_{k=1}^n \dfrac1{1-a_k} = 7 , find nn.

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