If `m` is a positive integer and `D_r=|[2r-1,m_(C_r),1],[m^2-1, 2^m, x+1],[sin^2(m^2),sin^2(m),sin^2(m+1)]| `Prove that`` `sum_(r=0)^m D_r=0`

If m is a positive integer and D_r=|(2r-1,\ ^m C_r,1),(m^2-1, 2^m ,m+1),(sin^2(m^2),sin^2(m),sin^2(m+1))| . Prove that sum_(r=0)^m D_r=0 .

If m is a positive integer and D_r=|(2r-1,\ ^m C_r,1),(m^2-1, 2^m ,m+1),(sin^2(m^2),sin^2(m),sin^2(m+1))| . Prove that sum_(r=0)^m D_r=0 .

If m is a positive integer and D_r=|2r-1\ ^m C_r1m^2-1 2^m m+1s in^2(m^2)s in^2(m)s in^2(m+1)| . Prove that sum_(r=0)^m D_r=0 .

Let m be a positive integer and Deltar = |[2r-1,.^mC_r,1],[m^2-1,2^m,m+1],[sin^2(m^2),sin^2m,sin(m^2)]| . Then the value of sum_(r=0)^m Deltar

Let m be a positive integer and Deltar = |[2r-1,.^mC_r,1],[m^2-1,2^m,m+1],[sin^2(m^2),sin^2m,sin(m^2)]| . Then the value of sum_(r=0)^m Deltar

Let m be a positive integer and Deltar = |[2r-1,.^mC_r,1],[m^2-1,2^m,m+1],[sin^2(m^2),sin^2m,sin(m^2)]| . Then the value of sum_(r=0)^m Deltar

Let m be a positive integer and Delta r=det[[m^(2)-1,*^(m)C_(r),1m^(2)-1,2^(m),m+1sin^(2)(m^(2)),sin^(2)m,sin(m^(2))]] of sum_(r=0)^(m)Delta r

If D_(r)=|{:(2r-1,""^(m)C_(r),1),(m^(2)-1,2^(m),m+1),(sin^(2)(m^(2)),sin^(2)(m),sin^(2)(m+1)):}| then find sum_(r=0)^(m)D_(r) .

Let m be a positive integer and Delta_(r)=|(2r-1,""^(m)C_(r),1),(m^(2)-1,2^(m),m+1),(sin^(2)(m^(2)),sin^(2)(m),sin^(2)(m+1))|(0lerlem) Then the value of sum_(r=0)^(m)Delta_(r ) is given by a)0 b) m^(2)-1 c) 2^(m) d) 2^(m)sin^(2)(2^(m))