If `x_1,x_2,x_3... x_n` are in H.P, then prove that `x_1x_2+x_2x_3+xxx-3x_4+..+x_(n-1)x_n=(n-1)x_1x_n`

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_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_(1),x_(2),x_(3)...x_(n) are in H.P,then prove that x_(1)x_(2)+x_(2)x_(3)+xx x-3x_(4)+...+x_(n-1)x_(n)=(n-1)x_(1)x_(n)

If x_(1), x_(2), x_(3) .................x_(n) are in H.P.then x_(1)x_(2)+x_(2)x_(3)+.......+x_(n-1)x_(n) =

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

Each of the numbers x_(1),x_(2),x_(3),...x_(n),n>=4 is equal to 1 or -1. Suppose x_(1)x_(2)x_(3)x_(4)+x_(2)x_(3)x_(4)x_(5)+x_(3)x_(4)x_(5)x_(6)+....x_(n-3)x_(n-2)x_(n-1)x_(n)+x_(n-2)x_(n-1)x_(n)x_(1)+x_(n-1)x then

Using mathematical induction prove that x+4x+7x+......+(3n-2)x=(1)/(2)n(3n-1)x