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]|` Show that `sum_(r=1)^n"Delta"_r`= Constant

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

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

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-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 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 Delta_(r) = |(2^(r -1),((r +1)!)/((1 + 1//r)),2r),(a,b,c),(2^(n) -1,(n +1)! -1,n(n +1))| , then sum_(r =1)^(n) Delta_(r) is equal to

If Delta_(r) = |(1,r,2^(r)),(2,n,n^(2)),(n,(n(n+1))/(2),2^(n+1))| , then the value of sum_(r=1)^(n) Delta_(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

Let n be a positive integer and Delta_(r)=|{:(r^(2)+r,r+1,r-2),(2r^(2)+3r-1,3r,3r-3),(r^(2)+2r+3,2r-1,2r-1):}| and sum _(r=1)^(n)Delta_(r)=an^(2)+bn+c find the value of a+b+c.

Evaluate: sum_(r=1)^n(3^r-2^r)