[" 17.Prove that "],[[1+a_(1),1,1],[1,1+a_(2),1],[1,1,1+a_(3)]|=a_(1)a_(2)a_(3)(1+(1)/(a_(1))+(1)/(a_(2))+(1)/(a_(3)))]

det[[1+a_(1),1,11,1+a_(2),11,1,1+a_(3)]]=a_(1)a_(2)a_(3)(1+(1)/(a_(1))+(1)/(a_(2))+(1)/(a_(3)))

(a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

prove that (1)/((a-a_(1))^(2)),(1)/(a-a_(1)),(1)/(a_(1))(1)/((a-a_(2))^(2)),(1)/(a-a_(2)),(1)/(a_(2))(1)/((a-a_(3))^(2)),(1)/(a-a_(3)),(1)/(a_(3))]|=(-a^(2)(a_(1)-a_(2))(a_(2)-a_(3))(a_(3)-a_(1)))/(a_(1)a_(2)a_(3)(a-a_(1))^(2)(a-a_(2))^(2)(a-a_(3))^(2))

" (iv) "|[1+a_(1),a_(2),a_(3)],[a_(1),1+a_(2),a_(3)],[a_(1),a_(2),1+a_(3)]|=1+a_(1)+a_(2)+a_(3).

If |(1+a_(1),a_(2),a_(3)),(a_(1),1+a_(2),a_(3)),(a_(1),a_(2),1+a_(3))|=0 then a_(1)+a_(2)+a_(3)=

If a_(1), a_(2), a_(3) ,…., a_(n) are the terms of arithmatic progression then prove that (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) + (1)/(a_(3)a_(4)) + ….+ (1)/(a_(n-1) a_(n)) = (n-1)/(a_(1)a_(n))

,1+a_(1),a_(2),a_(3)a_(1),1+a_(2),a_(3)a_(1),a_(2),1+a_(3)]|=0, then

Let a_(1),a_(2),a_(3), . . .,a_(n) be an A.P. Statement -1 : (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+(1)/(a_(3)a_(n-1))+ . . .. +(1)/(a_(n)a_(1)) =(2)/(a_(1)+a_(n))((1)/(a_(1))+(1)/(a_(2))+ . . .. +(1)/(a_(n))) Statement -2: a_(r)+a_(n-r+1)=a_(1)+a_(n)" for "1lerlen

Let a_(1),a_(2),a_(3), . . .,a_(n) be an A.P. Statement -1 : (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+(1)/(a_(3)a_(n-1))+ . . .. +(1)/(a_(n)a_(1)) =(2)/(a_(1)+a_(n))((1)/(a_(1))+(1)/(a_(2))+ . . .. +(1)/(a_(n))) Statement -2: a_(r)+a_(n-r+1)=a_(1)+a_(n)" for "1lerlen