If `A_(1), A_(3), ... , A_(2n-1)` are n skew-symmetric matrices of same order, then `B =sum_(r=1)^(n) (2r-1) (A_(2r-1))^(2r-1)` will be

If A_1, A_2, , A_(2n-1)a r en skew-symmetric matrices of same order, then B=sum_(r=1)^n(2r-1)(A^(2r-1))^(2r-1) will be symmetric skew-symmetric neither symmetric nor skew-symmetric data not adequate

If A_(1), A_(2),..,A_(n) are any n events, then

The value of sum_(r=0)^(3n-1)(-1)^r 6nC_(2r+1)3^r is

Prove that sum_(r=1)^n(-1)^(r-1)(1+1/2+1/3++1/r)^n C_r=1/n .

If a_(1),a_(2),a_(3),……a_(87),a_(88),a_(89) are the arithmetic means between 1 and 89 , then sum_(r=1)^(89)log(tan(a_(r ))^(@)) is equal to

A_(1),A_(2), …. A_(n) are the vertices of a regular plane polygon with n sides and O ars its centre. Show that sum_(i=1)^(n-1) (vec(OA_(i))xxvec(OA)_(i+1))=(1-n) (vec(OA)_2 xx vec(OA)_(1))

If a_(1), a_(2) , ……. A_(n) are in H.P., then the expression a_(1)a_(2) + a_(2)a_(3) + ….. + a_(n - 1)a_(n) is equal to

If a_(1), a_(2), ……., a_(n) are in A.P. with common differece d != 0 , then (sin d) [sec a_(1) sec a_(2) + sec a_(2) sec a_(3) + .... + sec a_(n - 1) sec a_(n)] is equal to

Let a_(1), a_(2) ...be positive real numbers in geometric progression. For n, if A_(n), G_(n), H_(n) are respectively the arithmetic mean, geometric mean and harmonic mean of a_(1), a_(2),..., a_(n) . Then, find an expression for the geometric mean of G_(1), G_(2),...,G_(n) in terms of A_(1), A_(2),...,A_(n), H_(1), H_(2),..., H_(n)