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Sir pls solve the following.
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Asked by rsudipto | 26 Dec, 2018, 11:34: AM
answered-by-expert Expert Answer
Each term in series is a square matrix of order 2×2.

First row, first column elements of each matrix are in GP,  i.e., 1+(1/2)+(1/4)+.......... ,

hence the respective element of first row, firsct column in matrix of sum is begin mathsize 12px style fraction numerator 1 minus open parentheses begin display style 1 half end style close parentheses to the power of infinity over denominator 1 minus begin display style 1 half end style end fraction space equals space 2 end style
First row, second column elements are constant 2
Second row, firsct column elements are in G.P. i.e., 6+2+(2/3)............, hence this element in matrix of sum is begin mathsize 12px style 6 fraction numerator 1 minus open parentheses begin display style 1 third end style close parentheses to the power of infinity over denominator 1 minus begin display style 1 third end style end fraction space equals space 9 end style
second row, second column element in all the terms is constant 4.
 
hence sum of series = begin mathsize 12px style open vertical bar table row 2 2 row 9 4 end table close vertical bar space equals space minus 10 end style
Answered by Thiyagarajan K | 27 Dec, 2018, 14:44: PM

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