If `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]|` , then find the value of `Delta`

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)=|(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

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=|[x,y,z],[2^r,2.3^r,3.4^r],[2(2^n-1),3.(3^n-1),4.(4^n-1)]| find the value of sumDelta_r

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)

If Delta_r=|(r,2r-1,3r+2),(n/2,n-1,a),(1/2n(n-1),(n-1)^2,1/2(n-1)(3n+4))| then the value of sum_(r=1)^(n-1) Delta_r (1) depends only on n (2) is independent of both a and n (3) depends only on a (4) depends both on a and n

If D_(r) = |(r,1,(n(n +1))/(2)),(2r -1,4,n^(2)),(2^(r -1),5,2^(n) -1)| , then the value of sum_(r=1)^(n) D_(r) , is