" 69.If "D_(r)=|[r,x,(n(n+1))/(2)],[2r-1,y,n^(2)],[3r-1,z,(n(3n+1))/(2)]|," then "sum_(r=1)^(n)D_(r)=

If D_r=|[r,1,(n(n+1))/(2)],[2r-1,4,n^2],[2^(r-1),5,2^(n)-1]| then, sum_(r=1)^n D_r

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

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 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

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

If S_r = |[2r,x,n(n+1)],[6r^2-1,y,n^2(2n+3)],[4r^3-2nr,z,n^3(n+1)]| then sum_(r=1)^nS_r does not depend on-

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 D_(r)=|(2^(r-1),2(3^(r-1)),4(5^(4-1))),(x,y,z),(2^(n)-1,3^(n)-1,5^(n)-1)| then sum_(r=1)^(n)D_(r)=

Let "T"_r=|[r ,x,(n(n+1))/2], [2r-1,y, n^2],[ 3r-2,z,(n(3n-1))/2]| .where T is the determinant of the given matrix, Then show that sum_(r=1)^n"T" _r=0 .