Consider three matrices A=[2141],B=[3423],  and  C=[3−4−23] . Then the value of the sumtr(A)+tr(ABC2)+tr(A(BC)24)+tr(A(BC)38)+.........+∞  is

BC=[3423][3−4−23]⇒BC=[1001]=I ⇒                  tr(A)+tr(ABC2)+tr(A(BC)24)+tr(A(BC)28)+.......+∞ =tr(A)+tr(A2)+tr(A22)+.... =tr(A)+12tr(A)+122tr(A)...... =tr(A)1−(1/2) =2tr(A)=2(2+1)=6