I have the vector vec(c) that is: vec(c) =(sum_(i=1)^n m_i vec r_i)/(sum_(i=1)^n m_i) where vec(r)_i i is a vector and m_i is a scalar I need to proof the folowwing equality for any vector vec(r) sum_(i=1)^n m_i|vec(r)-vec(r)_i|^2=sum_(i=1)^n m_1 |vec(r)_i-vec(c)|+m|vec(r)-vec(c)|^2

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$$\left[\begin{array}{cccc}1& 3& 0& -4\\ 2& 6& 0& -8\end{array}\right]$$

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b) ${\displaystyle f\left(n\right)=\sqrt{n^2+1}}$. 
c) ${\displaystyle f\left(n\right)=\frac{1}{n^2-4}}$.

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