If `"Delta"_r=|2^(r-1)2. 3^(r-1)4. 5^(r-1)x y z2^n-1 3^n-1 5^n-1|dot` Show that `sum_(r=1)^n"Delta"_r=Con s t a n t`

If D_r=|2^(r-1)2(3^(r-1))4(5^(r-1))x y z2^n-1 3^n-1 5^n-1| then prove that sum_(r=1)^n D_r=0.

If Delta_r=|[2^(r-1)2 , 3^(r-1) , 4. 5^(r-1)] , [x , y , z] , [2^n-1 , 3^n-1 , 5^n-1]|dot Show that sum_(r=1)^n Delta_r=Con s t a n t

Let "Delta"_r=|r-1n6(r-1)^2 2n^2 4n-2(r-1)^2 3n^3 3n^2-3n|dot Show that sum_(r=1)^n"Delta"_r is contant.

Let "Delta"_r=|r x(n(n+1))/2 2r-1y n^2 3r-2z(n(3n-1))/2| . Show that sum_(r=1)^n"Delta"_r=0 .

If Delta_(r)=det[[2^(r-1),2.3^(r-1),4.5^(r-1)alpha,beta,gamma2^(n)-1,3^(n)-1,5^(n)-1]], then find

Let Delta_r=|[r , x , (n(n+1))/2] , [2r-1 , y , n^2] , [3r-2 , z , (n(3n-1))/2]|dot Show that sum_(r=1)^n Delta_r=0

If ,y,z2^(r),2xx3^(r),3xx4^(r)2(2^(n)-1),3*(3^(n)-1),4*(4^(n)-1) Find the value of ,sum_(r=1)^(n)Delta_(r)

Let Delta_(r)=|(2^(r-1),2(3^(r-1)),4(5^(r-1))),(alpha, beta, gamma),(2^(n)-1,3^(n)-1,5^(n)-1)| for r=1,2,………..n . The sum_(r=1)Delta_(r) is