Consider three matrices $A=\left[\begin{array}{cc}2& 1\\ 4& 1\end{array}\right]$ , $B=\left[\begin{array}{cc}3& 4\\ 2& 3\end{array}\right]$ and $C=\left[\begin{array}{cc}3& -4\\ -2& 3\end{array}\right]$  then$tr\left(A\right)+tr\left(\frac{ABC}{2}\right)+tr\left(\frac{A{\left(BC\right)}^2}{4}\right)+tr\left(\frac{A{\left(BC\right)}^3}{8}\right)+\mathrm{......}=$

 

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