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` .

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

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-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-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]| . Show that sum_(r=1)^n Delta_r is contant.

Let Delta_r=|[r-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]| . Show that sum_(r=1)^n Delta_r is contant.

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)=

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 .

Let Delta_r=|{:(r,2r-1,3r-2),(n/2,n-1,a),((n(n-1))/2,(n-1)^2,1/2(n-1)(3n-4)):}| Show that sum_(r=1)^(n-1)Delta_r=0