Let n≥2 be a positive integer and let f(x) be the polynomial

1 - (x + x² + ... + xⁿ) + (x + x² + ... + xⁿ)² - ... + (-1)ⁿ(x + x² + ... + xⁿ)ⁿ.

Show that the coefficient of x^r in f(x) is zero, for 2≤r≤n.