we will calculate S=1+4q+9q^2+n^2q^(n-1) first
=(1-4)+(4-9)(1+q)+(9-16)(1+q+q^2)+...+((n-1)^2-n^2)(1+q+q^2+...+q^(n-2))+n^2(1+q+q^2+...+q^(n-1))
=-(3(q-1)/(q-1)+5(q^2-1)/(q-1)+...+(2n-1)q^(n-1)-1/(q-1))+n^2(q^n-1)/(q-1)
taking n to infinity
=1/(q-1)^2-2/(q-1)^3
replacing q with x and multiply by x we get
x/(x-1)^2-2x/(x-1)^3

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