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Proof of 2nd Derivative of a Sum of a Geometric Series

I am trying to prove how $$g''(r)=\sum\limits_{k=2}^\infty ak(k-1)r^{k-2}=0+0+2a+6ar+\cdots=\dfrac{2a}{(1-r)^3}=2a(1-r)^{-3}$$ or $\sum ak(k-1)r^(k-1) = 2a(1-r)^{-3}$. I don't know what I am doing ...