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|[(1)/(3),(1)/(5)],[(1)/(2),(1)/(7)]|...

|[(1)/(3),(1)/(5)],[(1)/(2),(1)/(7)]|

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Show that A= [(5,3),(-1,-2)] satisfies the equation x^2-3x-7=0 . Thus, find A^(-1) . a) [((2)/(7),(3)/(7)),((-1)/(7),(-5)/(7))] b) [(2,3),(-1,-5)] c) [((1)/(7),(1)/(7)),((-1)/(7),(-5)/(7))] d) [(3,-1),(1,2)]

(1)/(1.3)+(1)/(2)((1)/(3.5))+(1)/(3)((1)/(5.7))+....=

(1)/(1.3)+(1)/(2.5)+(1)/(3.7)+(1)/(4.9)+...=

(1)/(2)((1)/(5)+(1)/(7))-(1)/(4)((1)/(5^(2))+(1)/(7^(2)))+(1)/(6)((1)/(5^(3))+(1)/(7^(3)))-….oo=

(1)/(2)((1)/(5)+(1)/(7))-(1)/(4)((1)/(5^(2))+(1)/(7^(2)))+(1)/(6)((1)/(5^(3))+(1)/(7^(3)))-….oo=

If (1)/(1!9!)+(1)/(3!7!)+(1)/(5!5!)+(1)/(7!3!)+(1)/(9!1!)=(2^n)/(10!) , then n=