Each of the numbers x1, x2...., xn, n > 4, is equal to 1 or –1. Suppose,
x1x2x3x4 + x2x3x4x5 + x3x4x5x6 + ... + xn–3xn–2xn–1xn + xn–2xn–1xnx1+ xn–1xnx1x2 + xnx1x2x3 = 0, then,
Explanation:
The terms in the given expression are x1, x2, ... xn-1, xn.
There are n terms in the expression.
The only possible value of each of the terms is either 1 or –1.
For the given expression to be zero there should be even number of terms of which half the terms are –1 and the remaining are 1.
∴ n is even.
Hence, option (a).
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