S=404c_(4)-4c_(1)303c_(4)+c_(2)^(202)c_(4)-4c_(3)c_(4)=(101)^(k)

404C_(4)-^(303)C_(4)*^(4)C_(1)+^(202)C_(4)*^(4)C_(2)-^(101)C_(4)*^(4)C_(3)=

C_(2)H_(4),C_(4)H_(10), C_(3)H_(8),CH_(4)

8C_(4)+^(8)C_(3)=^(9)C_(4)

If the determinant of the matrix [(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))] is denoted by D, then the determinant of the matrix [(a_(1)+3b_(1)-4c_(1),b_(1),4c_(1)),(a_(2)+3b_(2)-4c_(2),b_(2),4c_(2)),(a_(3)+3b_(3)-4c_(3),b_(3),4c_(3))] will be -

1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)=

1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)=

("^(m)C_(0)+^(m)C_(1)-^(m)C_(2)-^(m)C_(3))+('^(m)C_(4)+^(m)C_(5)-^(m)C_(6)-^(m)C_(7))+..=0 if and only if for some positive integer k , m= (a) 4k (b) 4k+1 (c) 4k-1 (d) 4k+2