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Let A_(n) and B_(n) be square matrices of order 3, which are defined as : A_(n)=[a_(ij)] and B_(n)=[b_(ij)] where a_(ij)=(2i+j)/(3^(2n)) and b_(ij)=(3i-j)/(2^(2n)) for all i and j, 1 le i, j le 3. Ifl=lim_(n to oo) Tr. (3A_(1)+3^(2)A_(2)+3^(3)A_(3)+........+3^(n)A_(n)) andm=lim_(n to oo) Tr. (2B_(1)+2^(2)B_(2)+2^(3)B_(3)+.....+2^(n)B_(n)), then find the value of ((l+m))/(3) [Note : Tr (P) denotes the trace of matrix P.] |
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