Each of the numbers `x_1,x_2,x_3,....x_n, n>=4` is equal to `1` or `-1`. Suppose `x_1x_2x_3x_4+x_2x_3x_4x_5+x_3x_4x_5x_6+....x_(n-3)x_(n-2)x_(n-1)x_n+x_(n-2)x_(n-1)x_nx_1+x_(n-1)x_nx_1x_2=0` then

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

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. 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 N is any four digit number say x_1, x_2, x_3, x_4 , then the maximum value ofis equal to N/(x_1+x_2+x_3+x_4) is equal to

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) =