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

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-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.

If Dr=|[r,n+1,1],[r^2,2n-1,(2n+1)/3],[r^3,3n+2,(n(n+1))/2]|, show that sum_(r=1)^n Dr=0

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

Suppose n epsilon N and for 1lerlen Let Deltar=|(3r-2,2020,3n-1),(2r-1,2025,2n),(r,2029,n+1)| then 1/(3n) sum_(r=1)^(n)(Delta_(r)+6) is equal to __________

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