If `A_r=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|,` the value of `sum_(r=1)^n A_r` is (A) `n` (B) `2n` (C) `-2n` (D) `n^2`

If A_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 A_r is n (b) 2n (c) -2n (d) n^2

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 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, 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 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 Delta_(r )=|(r,2r-1, 3r-2),((n)/(2), n-1, a),((1)/(2)n(n-1), (n-1)^(2), (1)/(2)(n-1)(3n-4))| , then the value of sum_(r=1)^(n-1)Delta_(r )

Prove that sum_(r = 0)^n r^2 . C_r = n (n +1).2^(n-2)