Question 141

# Each of the numbers $$x_1, x_2, ... ,x_n$$ $$(n > 4)$$, is equal to 1 or -1. Suppose, $$x_1x_2x_3x_4 + x_2x_3x_4x_5 + x_3x_4x_5x_6 + ....... + x_{n-3}x_{n-2} x_{n-1}x_n x_1 + x_{n-1} x_n x_1 x_2 + x_n x_1 x_2x_3$$ = 0, then:

Solution

Since each term is either 1 or -1 . To be 0 we should have even terms and with n=even , no. of terms is even .