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, sum_(r=1)^n D_r

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 S_r=|{:(2r,x,n(n+1)),(6r^2-1,y,n^2(2n+3)),(4r^3-2nr,z,n^3(n+1)):}| , then the value of sum_(r=1)^(n)S_r is independent of

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 )

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 (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of sum_(r=0)^(n)a_(r) is