If `x_1,x_2,x_3….,x_n` are in H.P. prove that `x_1x_2+x_2x_3+x_3x_4+……….+x_(n-1)x_n=(n-1)x_1x_n`

If x_n =cos pi/(2^n) +isin pi/(2^n) , prove that x_1x_2x_3 x_oo=-1.

Q. if x_1,x_2......x_n are in H.P ., then sum_(r=1)^n x_r x_(r+1) is equal to : (A) (n-1)x_1 x_n (B) n x_1 x_n (C) (n+1)x_1 x_n (D) (n+2)x_1 x_n

If x_(1),x_(2),x_(3),…,x_(n) are the roots of the equation x^(n)+ax+b=0 , the value of (x_(1)-x_(2))(x_(1)-x_(3))(x_(1)-x_(4))…….(x_(1)-x_(n)) is

If x_(1),x_(2),x_(3),.,x_(n) are the roots of the equation x^(n)+ax+b=0 , the value of (x_(1)-x_(2))(x_(1)-x_(3))(x_(1)-x_(4))…….(x_(1)-x_(n)) is

If x_1, x_2, x_3,...... x _(2n) are in A.P , then sum _(r=1)^(2n) (-1)^(r+1) x_r^2 is equal to (a) (n)/((2n-1))(x _(1)^(2) -x _(2n) ^(2)) (b) (2n)/((2n-1))(x _(1)^(2) -x _(2n) ^(2)) (c) (n)/((n-1))(x _(1)^(2) -x _(2n) ^(2)) (d) (n)/((2n+1))(x _(1)^(2) -x _(2n) ^(2))

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that (1*2) C_(2) + (2*3) C_(3) + …+ {(n-1)*n} C_(n) = n(n-1) 2^(n-2) .

If x_1,x_2,x_3,... are positive numbers in G.P then logx_n, logx_(n+1), logx_(n+2) are in

If x_n=cos(pi/(2^n))+isin(pi/(2^n)) , prove that x_1x_2x_3........... x_oo=-1.

(1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - 2C_(1) + 3C_(2) - 4C_(3) + … + (-1)^(n) (n+1) C_(n) = 0

If n is even and nge4,x_(1),x_(2),...,x_(n)ge0 and x_(1)+x_(2)+...+x_(n)=1, then P=x_(1)x_(2)x_(3)…x_n cannot exceed