_The Cauchy-Schwarz Inequality states .+ a%)(b} + b3 + ...+ b,) (a,b1 + azb2 + ...+ a,bn)? < (aỉ + a3 + ...+ a)(b + b3 + ...+b) ,an,b1, b2, . .. , bn. Use this to prove the inequality for any real numbers a1, a2, .. (a1 + a2 +...+ an)² < n(a? + a, +...+ a). + a,).

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